https://orcid.org/0000-0003-1009-3629
SUMMARY
Seismic and electrical surveys are the most employed geophysical exploration applications for understanding the subsurface earth. Differential effective medium (DEM) models are the models to interpret the seismic and electrical survey data with the greatest success. However, cementation exponent and pore aspect ratio as the indispensable geometric parameters in the electrical and elastic DEM models are independent, making the models not suitable for the joint elastic–electrical modelling, a key requirement for the joint interpretation of seismic and electrical exploration data to better understand the increasingly complex hydrocarbon reservoirs. We show how cementation exponent and pore aspect ratio are correlated in three Berea sandstone samples with changing porosity resulting from varying pore pressure. We find that cementation exponent inverted from the electrical DEM model shows a strong positive linear correlation with pore aspect ratio obtained from the elastic DEM model as an implicit function of porosity-induced by increasing pore pressure. We also find that the established linear correlation can enable the DEM models to calculate one physical property (e.g. elastic or electrical) from the geometric parameter describing the other property (e.g. electrical or elastic). The results reveal how the elastic and electrical geometric parameters are linked, and provide a consistent microstructure that enables the existing elastic and electrical DEM models to be suitable for the joint elastic–electrical modelling of rocks undergoing varying pore pressure.
1 INTRODUCTION
Seismic and electrical surveys are the most employed geophysical exploration applications with most success for understanding the subsurface earth that reverses most of the mineral, energy and water resources needed by our society (Urish & Frohlich 1990; Constable & Srnka 2007; Alsadi 2017; Bertoni et al. 2020; Guo et al. 2020). Interpretation of the seismic and electrical survey data requires valid rock physics models that relate the seismic and electrical observations, respectively to the petrophysical properties of the underground rocks. Apart from the volume fractions and the corresponding physical properties of the various rock-forming ingredients, another key requirement in the development of the rock physics models is the geometric parameter that characterizes the relative microstructural arrangement of the ingredients (Mavko et al. 2009). Cementation exponent and pore aspect ratio are such commonly employed geometric parameters in inclusion based self-consistent (SC) and differential effective medium (DEM) models that are the simplest and most widely applied rock physics models (Mendelson & Cohen 1982; Sheng 1991; Berryman 1995; Cosenza et al. 2003; Berg 2007; Jensen et al. 2013; Aquino-López et al. 2015; Cilli & Chapman 2020; Markov et al. 2024).
With the hydrocarbon geophysical exploration heading to offshore deep water, onshore deep layer and unconventional reservoirs, single seismic or electrical method may not provide enough information about the increasingly complex reservoirs. Therefore, since seismic and electrical explorations contain independent but complementary reservoir attributes, they are jointly implemented to better characterize the complex hydrocarbon-bearing reservoirs (Wapenaar et al. 2008; Um et al. 2014; Kasdi et al. 2022). However, SC models have been evidenced not to be suitable for the joint elastic–electrical interpretation due to their lack of accuracy (Han et al. 2016). On the other hand, when interpreting the joint exploration data using DEM models that show the greatest success in modelling the electrical and elastic properties of rocks, respectively (Berg 2007; Cilli & Chapman 2020), a problem arises about the geometric parameter, that is, the pore aspect ratio and cementation exponent employed by the elastic and electrical DEM models are independent (Cilli & Chapman 2021). This results in inconsistent microstructures described by the elastic and electrical DEM models, thus making them not directly suitable for the joint elastic–electrical modelling. It is therefore logically interesting and important to wonder whether there are correlations between cementation exponent and pore aspect ratio so that the elastic and electrical DEM models are based on the same microstructure and hence can be applicable for the joint elastic–electrical modelling.
Cilli & Chapman (2020) invert for the pore and grain aspect ratios from experimentally measured P- and S-wave velocities and electrical conductivity, respectively using the elastic and electrical DEM models for samples with varying porosity, and find a power-law correlation between the inverted pore and grain aspect ratios and rock porosity. Cilli & Chapman (2020) link the obtained pore and grain aspect ratios based on their mutual dependence on porosity, and further establish a correlation between pore aspect ratio and cementation exponent, which is expressed as a function of grain aspect ratio using the model of Mendelson & Cohen (1982) with confirmed validity (Gelius & Wang 2008; Han et al. 2015). Although Cilli & Chapman (2020) do not show the explicit correlation between cementation exponent and pore aspect ratio, their idea of varying cementation exponent and pore aspect ratio with rock porosity (Kazatchenko et al. 2004; Aquino-López et al. 2015) inspires a potential way to correlate the independent geometric parameters to enable the existing elastic and electrical DEM models to be suitable for joint elastic–electrical modelling. However, the establishment of the correlation between cementation exponent and pore aspect ratio proposed by Cilli & Chapman (2020) is based on a range of samples with varying porosity, where in addition to the microstructure, parameters such as mineral composition among others also vary between samples. Therefore, the correlation between cementation exponent and pore aspect ratio in rocks caused exclusively by the varying microstructure remains to be explored.
This work aims to investigate how the cementation exponent and pore aspect ratio are correlated in specific samples with changing porosity resulting from varying pore pressure that is frequently encountered when exploiting the resources or storing CO2 or hydrogen in the subsurface reservoirs (Niaz et al. 2015; Osman et al. 2021). The simultaneously measured P-wave velocity, electrical conductivity and porosity of three Berea sandstone samples with varying pore pressure (Han et al. 2021) are selected for the investigation. The cementation exponent and pore aspect ratio of each sample are inverted as a function of pore pressure using electrical and elastic DEM models, respectively, and are then linked as an implicit function of the pore pressure induced variation in porosity. P-wave velocity and electrical conductivity are further modelled and compared with the measurements through cementation exponent and pore aspect ratio, respectively on basis of their established correlations. The joint velocity–conductivity is finally predicted and compared with the laboratory data using varying porosity as the only input parameter via the determined correlation between porosity and pore aspect ratio as well as the proposed correlation between pore aspect ratio and cementation exponent.
2 METHODS
2.1 Laboratory data set
We choose the laboratory data set collected by Han et al. (2021) on three porous Berea sandstone samples (i.e. HB3, B10.2 and B20, respectively) with P-wave velocity, electrical conductivity and porosity measured as a function of varying pore pressure.
The samples were cylinders with a diameter of approximately 2.54 cm and a length of about 5 cm. The dominant mineral comprising the samples with distinct porosity was quartz. The P-wave velocity and electrical conductivity were simultaneously measured on each fully saturated sample with 35 g l−1 NaCl brine (with conductivity of 4.69 S m−1) at a constant confining pressure of 50 MPa and increasing pore pressure from 1 to 40 MPa controlled by a pore pressure pump. The pore pressure pump also recorded the volume of brine injected into the sample to provide the needed pore pressure to an accuracy of ±0.0001 ml, which was employed to determine the rock porosity at each applied pore pressure through its initial porosity measured at the confining pressure of 50 MPa.
The P-wave velocity and conductivity were measured at the frequency of 0.5 MHz and 1 kHz, respectively, in a laboratory with temperature controlled at approximately 23 °C. The measurement errors were shown to be about ±0.8 per cent, ±0.2 per cent and ±0.01 porosity units for the P-wave velocity, electrical conductivity and porosity, respectively.
2.2 Inversion of cementation exponent and pore aspect ratio
To invert for the cementation exponent and pore aspect ratio from the measured electrical conductivity and P-wave velocity, respectively, we used the DEM models, namely the Hanai–Bruggeman (HB) model (Bruggeman 1935; Hanai 1960, 1961; Bussian 1983) for the electrical properties and Berryman's DEM model (Berryman 1995) for the effective elastic properties of two-phase rocks.
The HB model for the electrical conductivity (σ) of a rock consisting of water and solid grains with conductivity of σw and σg, respectively, and with water-filled porosity of ϕ gives
where m is the cementation exponent of the rock. In the limiting case of insulating solid grains (i.e. σg = 0), eq. (1) reduces to Archie's equation (Archie 1942) in the form of
Berryman's elastic DEM model (Berryman 1995) for the bulk and shear moduli (K and μ, respectively) of a rock with spheroidal pores (with porosity of ϕ) imbedded in the solid mineral background, is given as
with initial conditions K(0) = Km and μ(0) = μm, where Km and μm are the bulk and shear moduli of the initial mineral matrix, Ki and μi are the bulk and shear moduli of the pore inclusion, and the coefficients P(i) and Q(i) are geometric factors for the inclusion with an aspect ratio of α in each background medium (Berryman 1980; Mavko et al. 2009).
The inversion of the cementation exponent m and pore aspect ratio α at each pore pressure with determined porosity was achieved by setting them as fitting parameters to minimize the difference between the DEM calculated conductivity and P-wave velocity with their measured values, respectively. In the calculation, Km and μm were set to be 39 and 45 GPa, respectively with grain density of 2.63 g cm−3, and the bulk modulus, density and conductivity of the pore-filling brine were taken to be 2.5 GPa, 1.025 g cm−3 and 4.69 S m−1, respectively. These values were all consistent with those employed by Han et al. (2021). However, although the mineral properties and the brine conductivity may not vary much with pore pressure (Quist & Marshall 1968), pore pressure will significantly affect the elastic properties of the brine (Batzle & Wang 1992). Therefore, instead of using constant elastic properties for the brine (as has been done in Han et al. 2021), we calculated its bulk modulus and density as a function of pore pressure using the model given by Batzle & Wang (1992), and integrated these pore pressure dependent brine elastic properties in the inversion. The calculated bulk modulus and density with varying pore pressure at the laboratory temperature of 23 °C for the employed brine are illustrated in Fig. 1.
Calculated bulk modulus and density as a function of pore pressure for the employed 35 g l−1 NaCl brine at the temperature of 23 °C, using the model described by Batzle & Wang (1992).
2.3 Correlating cementation exponent and pore aspect ratio
The inverted cementation exponent and pore aspect ratio are both a function of the rock porosity at each pore pressure, in the form of
respectively. Cementation exponent and pore aspect ratio can then be correlated using porosity as the implicit link, as
The above way to correlate cementation exponent and pore aspect ratio is similar to that presented by Carcione et al. (2007) to link elastic velocity and electrical conductivity through rock porosity.
3 RESULTS
The methodology was applied to all the three samples, and the results were found to be similar. Therefore, we only show the results for the sample HB3, and the results for the other two samples B10.2 and B20 are given in the Supporting Information.
3.1 Variation of cementation exponent and pore aspect ratio with pore pressure and porosity
The inverted cementation exponent and pore aspect ratio with varying pore pressure are shown in Fig. 2. Both cementation exponent and pore aspect ratio reduce with increasing pore pressure and the reduction follows an exponential trend that can be described by the equation
where Z represents the geometric parameter (cementation exponent or pore aspect ratio), Pp is the pore pressure in MPa, and A, B and C are the best-fitting coefficients that are tabulated in Table 1.
The inverted cementation exponent and pore aspect ratio with varying pore pressure, and their best-fitting exponential curves.
The determined best-fitting coefficients for the exponential correlations between the geometric parameters and the varying pore pressure (Pp) and rock porosity (ϕ), respectively, as well as the correlation coefficients (R2) for the fit to the inverted geometric parameters.
| Correlation | A | B | C | R2 |
|---|---|---|---|---|
| m–Pp | 1.7675 | 0.0081 | 0.0441 | 0.9991 |
| α–Pp | 0.0682 | 0.0029 | 0.0484 | 0.9995 |
| m–ϕ | 1.7704 | 4.6800e−29 | 363.9737 | 0.9987 |
| α–ϕ | 0.0693 | 2.2832e−32 | 403.5506 | 0.9992 |
| Correlation | A | B | C | R2 |
|---|---|---|---|---|
| m–Pp | 1.7675 | 0.0081 | 0.0441 | 0.9991 |
| α–Pp | 0.0682 | 0.0029 | 0.0484 | 0.9995 |
| m–ϕ | 1.7704 | 4.6800e−29 | 363.9737 | 0.9987 |
| α–ϕ | 0.0693 | 2.2832e−32 | 403.5506 | 0.9992 |
The determined best-fitting coefficients for the exponential correlations between the geometric parameters and the varying pore pressure (Pp) and rock porosity (ϕ), respectively, as well as the correlation coefficients (R2) for the fit to the inverted geometric parameters.
| Correlation | A | B | C | R2 |
|---|---|---|---|---|
| m–Pp | 1.7675 | 0.0081 | 0.0441 | 0.9991 |
| α–Pp | 0.0682 | 0.0029 | 0.0484 | 0.9995 |
| m–ϕ | 1.7704 | 4.6800e−29 | 363.9737 | 0.9987 |
| α–ϕ | 0.0693 | 2.2832e−32 | 403.5506 | 0.9992 |
| Correlation | A | B | C | R2 |
|---|---|---|---|---|
| m–Pp | 1.7675 | 0.0081 | 0.0441 | 0.9991 |
| α–Pp | 0.0682 | 0.0029 | 0.0484 | 0.9995 |
| m–ϕ | 1.7704 | 4.6800e−29 | 363.9737 | 0.9987 |
| α–ϕ | 0.0693 | 2.2832e−32 | 403.5506 | 0.9992 |
The decrease in the pore aspect ratio with increasing pore pressure can be caused by the opening of low aspect ratio compliant pores with increasing pore pressure (Shapiro 2003; Han et al. 2021). Since the compliant pores with low aspect ratios are gradually opening, porosity will increase (as illustrated in Fig. 3), and the determined pore aspect ratio that is an effective representation of the pore system with varying aspect ratios will decrease. The newly opened compliant pores can help to bridge the nearby stiff pores, and hence will improve the connectivity of the pore network. The improved pore connectivity will facilitate the transportation of the electrical current, and therefore the cementation exponent of the sample that represents implicitly the ‘connectedness’ of the pore network for the availability of pathways for electrical flow will reduce (Glover 2009; Yue 2019; Han et al. 2020).
Variation of the measured rock porosity with pore pressure and its best-fitting linear curve.
It is understandable that the opening of the compliant pores with increasing pore pressure will improve the rock porosity, and it is interesting that the increase in the porosity shows a strong linear dependence on pore pressure, as shown in Fig. 3. This linear dependence seems to contradict the effects of confining pressure that has been shown to exponentially reduce the rock porosity (Coyner 1984; Eberhart-Phillips et al. 1989; David & Zimmerman 2012). However, the seeming contradiction can be explained and reconciled in terms of the different ranges in the differential pressure (the difference between confining pressure and pore pressure) of the various experiments. In the investigation of confining pressure effects on the rock porosity, pore pressure is usually controlled at a very small value, and the applied confining pressure can be roughly regarded as the differential pressure. In this case, porosity shows an exponential reduction with increasing differential pressure. However, the exponential variation exhibits only in the low differential pressure range (usually below about 20 MPa or even lower), and after that the reduction in the porosity tends to be linear (Coyner 1984; Eberhart-Phillips et al. 1989). On the other hand, in the experiment to collect the data employed in this work (Han et al. 2021), confining pressure is kept at 50 MPa with pore pressure increasing from 1 to 40 MPa. This gives rise to varying differential pressure between 10 and 49 MPa, which might be sitting in the high differential pressure range, and therefore porosity shows a linear variation.
We have shown that both cementation exponent and pore aspect ratio decrease exponentially while porosity increases linearly with increasing pore pressure. It is therefore reasonable to speculate an exponential reduction of cementation exponent and pore aspect ratio with increasing porosity caused by the increasing pore pressure. This is confirmed by the results plotted in Fig. 4. The exponential reduction of the cementation exponent and pore aspect ratio with increasing porosity can be fitted by an equation similar to eq. (6), in the form of
where Z stands for cementation exponent or pore aspect ratio, ϕ is the rock porosity and A, B and C are the best-fitting coefficients and are listed in Table 1.
The inverted cementation exponent and pore aspect ratio with the variation in the pore pressure induced changes in porosity, and their best-fitting exponential curves.
The exponential correlations between the geometric parameters and porosity look similar to their correlations with pore pressure. However, their potentials for the modelling of the elastic and electrical rock properties are different. As mentioned above, the information needed by the DEM models to calculate the physical rock properties includes the volume fractions and the corresponding physical properties (i.e. elastic properties of the materials are required to compute the elastic rock properties) of the rock-forming materials, and the geometric parameter describing the microstructure of the rock (Mavko et al. 2009). We have specified the cementation exponent and pore aspect ratio as the geometric parameters for the electrical and elastic rock modelling, respectively. In addition, since we are considering two-phase rocks, the volume fractions of the materials can be ready as long as the rock porosity is known. Therefore, we only need to further know the physical properties of the materials for the effective medium modelling. However, although the physical characteristics of the minerals are not dependent on pore pressure, the elastic and electrical properties of the pore brine show different dependence on pore pressure.
Quist & Marshall (1968) demonstrate that the conductivity of brine does not vary much with the applied pore pressure. Therefore, the correlation between cementation exponent and porosity illustrated in Fig. 4 can be directly employed to model the electrical properties of the rock with varying pore pressure, provided that the brine conductivity is available. However, the elastic properties of brine have been shown to vary dramatically with pore pressure, as demonstrated by Batzle & Wang (1992), and shown in Fig. 1. Hence, the pore aspect ratio to porosity correlation given in Fig. 4 will not be applicable for the elastic modelling, because it lacks the information of pore pressure that determines the elastic properties of the brine. In this case, we have to base on the obtained correlation between pore aspect ratio and pore pressure in Fig. 2, together with the dependence of porosity on pore pressure illustrated in Fig. 3 and the pore pressure dependent brine elastic properties (as shown in Fig. 1) to model the variation of the elastic rock properties with pore pressure.
3.2 Correlation between cementation exponent and pore aspect ratio
Since both cementation exponent and pore aspect ratio decrease exponentially with the pore pressure induced increase in rock porosity, it can be expected that these two geometric parameters should be positively correlated. The results in Fig. 5 confirm this positive correlation, and surprisingly show a strong linear trend for the positive correlation. The linear correlation not only reveals how naturally the elastic and electrical geometric parameters are correlated, but also provides a great potential for the joint elastic–electrical modelling. This is because the linear correlation represents the simplest way that cementation exponent and pore aspect ratio are correlated, and therefore once the line-determining parameters (i.e. the slope and the y-axis intercept) are obtained, one geometric parameter can be easily estimated from the other. This will allow the elastic rock properties to be modelled based on the electrical geometric parameter and the electrical rock properties to be modelled from the elastic geometric parameter, thus enabling the joint elastic–electrical modelling on basis of a consistent rock microstructure.
Correlation between cementation exponent and pore aspect ratio as an implicit function of the pore pressure induced variation in rock porosity, and its best-fitting linear curve.
3.3 Potential for the joint elastic–electrical modelling
We have established the correlation between cementation exponent and pore aspect ratio using pore pressure induced variation in the rock porosity as the link, and have also analysed the potential of the relationship for the joint elastic–electrical modelling. Before testing such potential, we first investigate whether the elastic velocity can be calculated from the cementation exponent and whether the electrical conductivity can be computed from the pore aspect ratio through the obtained correlation between the geometric parameters.
The comparison of the measured P-wave velocity and electrical conductivity as a function of porosity resulting from varying pore pressure with their modelled values is shown in Fig. 6. In the modelling, electrical conductivity is calculated from pore aspect ratio using the correlation given in Fig. 5 on basis of the measured porosity at each pore pressure. On the other hand, P-wave velocity is computed using cementation exponent from the correlation, in combination with the measured porosity and the pore pressure dependent elastic properties of brine. It is encouraging that the model calculations compare satisfactorily well with the measured data, which lays the foundation for the joint elastic–electrical modelling.
Comparison of the measured P-wave velocity and electrical conductivity with their modelled values using cementation exponent and pore aspect ratio, respectively, through the obtained correlation between cementation exponent and pore aspect ratio.
Having demonstrated that the obtained correlation between the geometric parameters can enable the DEM models to calculate elastic rock properties from the microstructure usually employed to describe the electrical properties, and vice versa, we further investigate whether the correlation can be used for the joint elastic–electrical modelling. The modelling results are shown in Fig. 7 in comparison with the laboratory data. The only input parameter in the modelling is the varying rock porosity in the measured pore pressure range. The varying porosity is employed to estimate cementation exponent using the relation given in Fig. 4, and the determined cementation exponent is in turn employed to compute the pore aspect ratio through the presented correlation between cementation exponent and pore aspect ratio given in Fig. 5. The varying rock porosity is also employed to invert for the pore pressure (on basis of the relationship illustrated in Fig. 3), which is based on to further calculate the varying elastic properties of brine with pore pressure for the modelling of the elastic properties of the rock. The determined pore aspect ratio and brine elastic properties, and cementation exponent are finally employed in combination with the varying porosity to calculate the elastic and electrical rock properties, respectively, which are linked through porosity as the joint elastic–electrical modelling results (Carcione et al. 2007; Jensen et al. 2013; Han et al. 2020). The excellent agreement between the modelling results and the experimental data confirms and validates the potential of the correlation between cementation exponent and pore geometry with varying pore pressure for the joint elastic–electrical modelling of porous sandstones.
Comparison of the measured joint elastic–electrical properties as an implicit function of varying pore pressure, with their modelled values through the obtained correlation between cementation exponent and pore aspect ratio. The only input parameter in the modelling is the varying rock porosity in the measured pore pressure range. The varying rock porosity is used to calculate the cementation exponent, which is further used to determine the pore aspect ratio. The varying rock porosity is also employed to invert for the pore pressure, which is used to calculate the pore pressure dependent elastic properties of the pore-filling brine.
4 DISCUSSION
We have established the correlation between cementation exponent and pore aspect ratio in three Berea sandstone samples as an implicit function of porosity induced by varying pore pressure. We have also demonstrated that the developed correlation can enable the DEM models to calculate one physical property (e.g. elastic or electrical) from the geometric parameter describing the other property (e.g. electrical or elastic). In the joint elastic–electrical modelling, we chose to first estimate the cementation exponent from the varying porosity with pore pressure, and then determine the pore aspect ratio from the estimated cementation exponent through the established correlation. The determined geometric parameters were finally employed together with the pore pressure dependent rock porosity and elastic brine properties for the joint elastic–electrical modelling. This procedure is preferred due to the fact that the errors in the inverted cementation exponent (about ±0.06 per cent) from the measured rock conductivity with errors of around ±0.2 per cent are much better than those in the obtained pore aspect ratio (with errors of approximately ±3 per cent) from the measured rock velocity with errors of around ±0.8 per cent. The estimation of the pore aspect ratio from the cementation exponent with greater accuracy will help to minimize the errors in the joint elastic–electrical calculations. However, it should be pointed out that the correlation is established in each specific sample with varying pore pressure, and hence might not be applied to other samples. This is because the linear correlation between cementation exponent and pore aspect ratio can differ between samples, and what determines the linear correlation and what are the controlling factors of the linear dependence of porosity on pore pressure are still key questions to answer. A thorough investigation and clarification of these questions to enable the application of the correlation to a wider range of samples will form the topics of our future studies.
It should also be noted that the elastic DEM models are designed for the high-frequency limit elastic properties of rocks (Berryman 1995; Mavko et al. 2009; Cilli & Chapman 2021), whereas the P-wave velocities employed in this work are measured at a finite frequency of about 0.5 MHz (Han et al. 2021). In the high-frequency limit, the fluid does not have time to flow between pores with different compliance so that it is trapped and isolated in the pores, making the elastic moduli of the rock the highest (Jones 1986). On the other hand, when an elastic wave with finite frequency is applied, fluid flow can happen between the differently deformed pores resulting from the local pressure gradients of the passing wave, and the flowing fluid will contribute less to the rock moduli, leading to frequency dependent but always lower elastic moduli (Mavko & Jizba 1991; Gurevich et al. 2010). This frequency gap between the measurements and the model requirements indicates that the inverted pore aspect ratio may not be the effective representation of the real pore system. Fortunately, in the forward elastic modelling based on the cementation exponent, the cementation exponent is determined through its correlation with the inverted pore aspect ratio from the DEM models. This inversion and forward cycle will help to exclude the frequency effects and hence ensures that the pore aspect ratio, even though is not representing the real pore microstructure, will allow the DEM models to simulate the elastic properties at the measured finite frequency. The same applies to the determined cementation exponent.
Although the approach has removed the frequency effects in the DEM models, it should be noted that we have assumed insulating grain minerals in the rock to use the electrical DEM models (as mentioned above when introducing the models). This assumption can be satisfied in our clean Berea sandstone samples, but may not be fulfilled in clay-rich sandstones that are widely distributed. The electrochemical interactions of the mineral-water system associated with clay minerals will give rise to an excess surface conductivity that makes additional contribution to the rock conductivity through pore fluid (Revil 2013; Ko et al. 2023). The additional surface conductivity might be modelled by assigning a grain conductivity in the DEM models. However, how this grain conductivity can be quantified and whether the cementation exponent is still appropriately representing the microstructure are still questions we are facing. Therefore, before solving these problems it should be clearly pointed out that the presented correlation between cementation exponent and pore aspect ratio and the further joint elastic–electrical modelling through this correlation are based on the assumption of clean porous rocks with their physical properties theoretically computed using the two-phase DEM models.
5 CONCLUSIONS
We have demonstrated that cementation exponent inverted from electrical DEM models shows a strong positive linear correlation with pore aspect ratio obtained from elastic DEM models as an implicit function of porosity induced by increasing pore pressure. The linear correlation can enable the changes in cementation exponent resulting from varying pore pressure to be easily estimated from the variations in pore aspect ratio, and vice versa. We have also demonstrated that the established linear correlation can enable the DEM models to calculate one physical property (e.g. elastic or electrical) from the geometric parameter describing the other property (e.g. electrical or elastic). The correlation reveals how the elastic and electrical geometric parameters are linked, and provides a consistent microstructure that enables the existing elastic and electrical DEM models to be suitable for the joint elastic–electrical modelling of rocks experiencing varying pore pressure.
DATA AVAILABILITY
Data associated with this research are stored in the Open Science Frame work available at https://osf.io/wrcyt.
ACKNOEWLEDGEMENTS
The authors would like to acknowledge the financial support received from the National Natural Science Foundation of China (42174136 and 41821002), the Shandong Provincial Natural Science Foundation, China (ZR2021JQ14) and the Fundamental Research Funds for the Central Universities (22CX07004A).
