Characteristics analysis of 3D marine CSEM response using the vector finite element method with secondary formulation

Abstract

In recent years, the controlled-sources electromagnetic method has been widely applied for oil and metallic ore exploration. It is necessary to study the effects of the constituents and microstructure in pyrite-bearing hydrocarbon-bearing reservoir sandstones on 3D marine controlled source electromagnetic sounding, so as to improve the accuracy of the marine controlled sources electromagnetic (MCSEM) Method. In this paper, we present a new finite element algorithm for 3D MCSEM modeling, which is based on unstructured grids. In the modeling, we adopted the secondary formulation for the quasi-static variant of Maxwell’s equation, so that the source singularity could be avoided effectively. We first applied the four-phase incremental model to calculate the conductivity of the pyrite-bearing hydrocarbon. This is of use in studying the electrical conductivity of pyrite-bearing sandstones. The finite element equations were solved by means of the preconditioned IDR(s) method. We applied our algorithm to calculate the response of various key parameters of MCSEM (i.e. pyrite content, porosity, pyrite conductivity, grain aspect ratio and water saturation). The results of the modeling show the performance of the algorithm, and are expected to assist in future CSEM data interpretation when a pyrite-bearing sandstone reservoir is encountered.

Keywords

Secondary formulation IDR(s)marine controlled sources electromagnetic multi-phase incremental model unstructured mesh vector finite element method

1. Introduction

The marine controlled source electromagnetic (MCSEM) method has rapidly developed to be a complementary tool for emerging seismic exploration related to offshore hydrocarbon exploration. The 3D MCSEM modeling and inversion problem is a hot research issue around the world. The technique of MCSEM modeling has been widely developed, including the 1DForward technique [1, 2, 3, 4, 5], 2D Forward technique [6, 7, 8, 9, 10] and 3D Forward technique [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]. However, most of the conventional marine controlled source electromagnetic modeling has either not considered the influence of the composition and structure of the rocks on electromagnetic (EM) fields, or only considered it in terms of the frequency relativity to study rock conductivity [22, 23, 24, 25, 26, 27, 28, 29]. For example, we may study the effects of the corresponding parameters of the complex resistivity model on marine controlled source electromagnetic (EM) fields by the introduction of various complex resistivity models, i.e. induced polarization effect. However, they fail to directly address the problem of how pyrite affects the low frequency electrical properties of reservoir sandstones, which can be further employed to study the response of low-frequency marine controlled source electromagnetic (CSEM) exploration. Therefore, it is of great theoretical significance and practical value to improve the accuracy of the data interpretation by researching the influence of pyrite or other mineral components in the reservoir on marine controlled source electromagnetic fields. One of the key factors by which to improve the accuracy of the CSEM data interpretation is using the petro-physical model to reasonably link the electrical conductivity of the sedimentary rocks to their components. At present, the petro-physical models (equations) of an effective medium mainly include Archie’s equation [30], Hanai-Bruggeman (HB) equation [31, 32], and Asami equation [33]. However, these equations were only developed for a two-phase medium, and cannot be applied to a multi-phase medium that is closer to the actual situation. Therefore, in order to solve this problem, Han et al. proposed the petro-physical incremental model, which is based on the Asami equation with an incremental model [34], while it can display some basic structure and lithologic characteristics of rocks and ores in the macro scale. In addition, the parameters are related to the physical properties of rocks and ores, which provide a quantitative analysis method by which to research the electrical conductivity of multi-phase rocks and ores.

On the basis of previous work, in this study we employ the multi-phase incremental model to realize the 3D marine controlled source electromagnetic modeling. We also comprehensively study various parameters (porosity, content of pyrite, pyrite grains conductivity, aspect ratio and water saturation), along with their effects on the pyrite reservoir conductivity and the components of marine controlled source electromagnetic fields, so that the marine controlled source electromagnetic exploration theory may be further enriched.

2. Introduction of incremental model

2.1 Asami equation

The Asami equation is a two-phase effective medium model proposed by Asami in 2007, based on the Maxwell-Wagner theory and a large number of specimens. The equation is as follows:

$\displaystyle\phi=\left(\frac{\sigma_{a}(1+3L)+\sigma_{g}(2-3L)}{\sigma(1+3L)+% \sigma_{g}(2-3L)}\right)^{C}\left(\frac{\sigma-\sigma_{g}}{\sigma_{a}-\sigma_{% g}}\right)\left(\frac{\sigma_{a}}{\sigma}\right)^{3T}$ (1)

where $\sigma$ , $\sigma_{a}$ and $\sigma_{g}$ are the conductivity of effective medium, background medium, and impurity inclusion, respectively. $\Phi$ is volume percentage of inclusions. $\phi=1-\Phi$ , is the volume percentage of the background medium, which is the same as the initial concentration of composition (C/N). In the following section, we will introduce the calculation process of the initial concentration of composition in detail. $L_{x}$ , $L_{y}$ and $L_{z}$ denote the polarization factor of the $x$ , $y$ and $z$ direction of particles, respectively. Among the polarization factors, they satisfy the following:

$\displaystyle L=L_{x}=L_{y}=(1-L_{z})/2,$ $\displaystyle T=L(1-2L)/(2-3L),$ $\displaystyle C=2(1-3L)^{2}/(2-3L)/(1+3L).$

For ellipsoid inclusions with the ratio of long axes and short axes $\underline{a}<1$ , we obtain:

$\displaystyle L_{z}=\frac{1}{\left(1-\alpha^{2}\right)}-\alpha/\left(1-\alpha^% {2}\right)^{3/2}{\cos}^{-1}\alpha.$ (2)

We use the Newton method to solve Eq. (1) and obtain the conductivity of the effective medium.

2.2 Multi-phase incremental model

In the case of particle aspect ratio ( $a=$ 1, $L_{z}=$ 1/3), the Asami effective conductivity equation may be reduced to the well-known Hanai-Bruggeman (HB) effective conductivity equation [31, 32]. In addition, if the conductivity $\sigma_{g}$ of the inclusion is neglected, then the Asami effective conductivity equation can be further simplified to Archie’s equation [30]. However, these are based on the effective model of a two-phase medium only, and are unsuitable for a multi-phase medium (such as water-rich pyrite-rich hydrocarbon reservoir). Therefore, Asami et al. proposed an incremental model which was more in line with the real situation of the multi-phase medium, in order to compensate for this need [34].

Figure 1.

Schematic diagram showing the steps used in the first increment in the incremental model.

Figure 2.

Plots of the conductivity of pyrite-bearing sandstones with different parameters.

Without loss of generality, we use the four-phase incremental model as an example. Figure 1 is the first increment of this model. First, assuming that the initial concentration of three minerals which are divided into N (i.e. incremental number) parts are C ${}_{2}$ , C ${}_{3}$ and C ${}_{4}$ , respectively, i.e. the respective concentrations of each component are C ${}_{2}$ /N, C ${}_{3}$ /N and C ${}_{4}$ /N. Then, using seawater as the initial background medium, and according to a certain order, each component of the medium (C ${}_{2}$ /N, C ${}_{3}$ /N, C ${}_{4}$ /N) is added to form an effective medium. After all three of the inclusion phases (i.e. hydrocarbon, pyrite and quartz) are added in the first increment where water is the staring background medium, the next increment then begins until the incremental number n is reached. The Asami equation (Eq. (1)) 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 ${}_{2}$ /N, C ${}_{3}$ /N, C ${}_{4}$ /N) and incremental number N based on the equations given in the Appendix. For the sake of simplicity, we only researched the electrical conductivity and characteristics on marine controlled source electromagnetic responses caused by the compositions (i.e. water, pyrite, quartz and hydrocarbon) and structure of marine sedimentary rocks.

Figure 2 shows the conductivity curves of the effective medium, where we change the pyrite conductivity, water saturation, volume fraction of pyrite and aspect ratio of the particles. In Fig. 2a, we set them as fitting rock parameters. The respective conductivities of the formation water ( $\sigma_{w}$ ), quartz ( $\sigma_{qz}$ ) and gas ( $\sigma_{\textit{gas}}$ ) are 3.3, 0.001 and 0.0001. The aspect ratio of the quartz particles ( $a_{qz}$ ) and gas ( ${a}_{\textit{gas}}$ ) both are 0.2. The water saturation ( ${S}_{w}$ ) and the volume fraction of pyrite ( $V_{py}$ ) is 0.02. The conductivity of pyrite ( $\sigma_{py}$ ) is 1.5: 1.5: 15. Unlike Fig. 2a, in Fig. 2b the conductivity of pyrite ( $\sigma_{py}$ ) is 15, and the water saturation ( ${S}_{w}$ ) is 0.05: 0.5: 1. The parameters in Fig. 2c are $V_{py}=$ 0.002: 0.02: 0.1 and ${\sigma}_{py}=$ 15, while those in Fig. 2d are $a_{py}=$ 0.02: 0.2: 1, $\sigma_{py}=$ 15. The remaining parameters are the same as in Fig. 2a.

From Fig. 2a, one can see that, under the same porosity, the effective conductivity changes little with increasing pyrite conductivity, yet the effective conductivity increases with increasing porosity. According to Fig. 2b, under the same water saturation, the effective conductivity increases with increasing porosity. In the case of the same porosity, the effective conductivity increases with increasing water saturation. Figure 2c shows that, at the same porosity, the effective conductivity denotes an approximate linear increase with the volume fraction of pyrite. In the same volume percentage of pyrite, the effective conductivity increases with increasing porosity. From Fig. 2d one can see that, under the same porosity conditions, the effective conductivity generally increases along with the pyrite aspect ratio. Moreover, in the case of the same aspect ratio the effective conductivity increases with the increasing porosity.

3. Forward theory

3.1 Governing equation

In geophysical electromagnetic prospecting, low frequency electromagnetic signals are typically transmitted. When the displacement current is neglected, and the sinusoidal harmonic time factor $e^{i\omega t}$ is employed, the Maxwell equations can be written in the following form [35]:

$\displaystyle\nabla\times E=i\omega\mu_{0}H,$ (3) $\displaystyle\nabla\times H=J_{s}+\sigma E,$ (4)

where $\omega$ denotes angular frequency, $\mu_{0}$ presents the permeability of vacuum, $J_{s}$ is the current distribution of the source, and $\sigma$ is the conductivity. To study the effects of the key parameters for the MCSEM modeling, we simply need to use the equivalent conductivity $\sigma_{e}$ , which is obtained by using Eq. (1) to replace the original conductivity $\sigma$ .

To avoid the singularity of the source, the entire field is decomposed into a primary field and secondary field. The conductivity is then decomposed into background conductivity and anomalous conductivity, and two equations are obtained as follows:

$\displaystyle E=E_{p}+E_{s},$ (5) $\displaystyle\sigma=\sigma_{s}+\Delta\sigma.$ (6)

According to Eqs (3)–(6), we can further deduce the differential equation of the anomalous field:

$\displaystyle\nabla\times\nabla\times E_{s}-i\omega\mu_{0}\sigma E_{s}=i\omega% \mu_{0}\Delta\sigma E_{p}.$ (7)

From Eq. (7), for a general layered earth model, the background field $E_{p}$ can be computed semi-analytically by using a digital filter to calculate the Hankel transforms. Equation (7) can be solved by the finite difference method, finite element method, integral equation method or boundary element method. After solving the secondary electric field, the secondary magnetic field can then be calculated by the following equation, after which the total magnetic field can be obtained:

$\displaystyle H_{s}=\frac{1}{i\omega\mu_{0}}\nabla\times E_{s}.$ (8)

3.2 Boundary conditions

When the boundary is located far enough away from the target area, the secondary field can be approximated as zero. For the sake of simplicity, we apply the Dirichlet boundary conditions as follows:

$\displaystyle n\times E_{s}=0,$ (9)

where $n$ is the normal unit vector on the boundary.

3.3 Vector finite element analysis

In this paper, Whitney type vector basis functions are used to carry out spatial discretization with unstructured tetrahedral mesh [36]:

$\displaystyle{N}_{i}^{e}=\left(L_{i1}^{e}{\nabla}L_{i2}^{e}-L_{i2}^{e}{\nabla}% L_{i1}^{e}\right)l_{i}^{e},$ (10)

where $L_{i1}^{e}$ is the weight function of the first nodes on the edge of I of unit e, $L_{i2}^{e}$ is the weight function of second nodes on the edge of I of unit e, and $l_{i}^{e}$ is the length of the edge of I of unit e. The schematic diagram between the edge and node of the 3D tetrahedron element is shown in Fig. 3. Assuming that the electric field on the edge of I is $E_{i}^{e}$ , the electric field in the tetrahedral element can then be expressed as follows:

$\displaystyle{E}^{e}=\sum{{}_{j=1}^{6}}{N_{j}^{e}E_{j}^{e}}.$ (11)

Figure 3.

The number sketch map of nodes and edges of tetrahedron.

Equation (7) can be expressed as a form of weak solutions with the Galerkin method:

$\displaystyle{R}_{i}^{e}=\iiint_{\Omega_{e}}N_{i}^{e}\cdot\left[\nabla\times% \nabla\times{E}_{{s}}^{{e}}-i\omega\mu\sigma{E}_{{s}}^{e}-i\omega\mu\Delta% \sigma{E}_{{p}}^{e}\right]dV.$ (12)

According to the first vector Green function, we obtain the following:

$\displaystyle\iiint_{\Omega_{e}}{{N}_{i}^{e}\cdot\left[{\nabla\times\nabla% \times}{{E}}_{{s}}^{{e}}\right]dV}=\iiint_{\Omega_{e}}{\left({{\nabla\times}{N% }}_{i}^{e}\right)\cdot\left({\nabla\times}{{E}}_{{s}}^{{e}}\right)dV}$ (13) $\displaystyle\quad-\iiint_{\Gamma_{e}}{\left({{{n}\times}{N}}_{i}^{e}\right)% \cdot\left({\nabla\times}{{E}}_{{s}}^{{e}}\right)ds}.$

Considering that the Area division of Eq. (3.3) can be ignored when the boundary of the region is automatically defined and the outer boundary is artificially defined, Eq. (3.3) can be simplified as follows:

$\displaystyle\iiint_{\Omega_{e}}{N_{i}^{e}\cdot\left[\nabla\times\nabla\times{% E}_{{s}}^{{e}}\right]dV}=\iiint_{\Omega_{e}}{\left(\nabla\times N_{i}^{e}% \right)\cdot\left(\nabla\times{E}_{{s}}^{{e}}\right)dV}.$ (14)

Deriving Eq. (14) into Eq. (7), we obtain the following:

$\displaystyle{R}_{{i}}^{e}=\iiint_{\Omega_{e}}{\left[\left(\nabla\times N_{i}^% {e}\right)\cdot\left(\nabla\times{E}_{{s}}^{{e}}\right)-i\omega\mu\sigma N_{i}% ^{e}\cdot{E}_{{s}}^{e}-i\omega\mu\Delta\sigma{N_{i}^{e}\cdot{E}}_{{p}}^{e}% \right]dV,}$ (15)

where

$\displaystyle{E}_{s}^{e}=\sum{{}_{j=1}^{6}}N_{j}^{e}E_{s_{j}}^{e},$ (16) $\displaystyle{E}_{p}^{e}=\sum{{}_{k=1}^{6}}N_{k}^{e}E_{p_{k}}^{e}.$ (17)

Equation (15) can be rewritten with Eqs (16) and (17):

$\displaystyle{R}_{{i}}^{e}=\!\sum{{}_{j=1}^{6}}\!\iiint_{\Omega_{e}}\!{\left[% \left(\nabla\times N_{i}^{e}\right)\cdot\left(\nabla\times{N}_{j}^{e}\right)E_% {s_{j}}^{e}-i\omega\mu\sigma{N}_{i}^{e}\cdot{N}_{j}^{e}E_{s_{j}}^{e}-i\omega% \mu\Delta\sigma{{N}_{i}^{e}\cdot{{E}}}_{{p}}^{e}\right]dV}.$ (18)

The weighted residual matrix equation of unit $e$ can be written in the following form:

$\displaystyle{R}^{{e}}=K^{e}E_{s}^{e}-b^{e},$ (19)

With

$\displaystyle K_{ij}^{e}=\iiint_{\Omega_{e}}{\left[\left(\nabla\times N_{i}^{e% }\right)\cdot\left(\nabla\times N_{j}^{e}\right)-i\omega\mu\sigma N_{i}^{e}% \cdot N_{j}^{e}\right]dV}$ (20) $\displaystyle{b}_{{i}}^{e}=\iiint_{\Omega_{e}}{\left[{i\omega\mu\Delta\sigma}{% N_{i}^{e}\cdot{E}}_{{p}}^{e}\right]dV}=\sum{{}_{k=1}^{6}}\iiint_{\Omega_{e}}{% \left[{i\omega\mu\Delta\sigma}N_{i}^{e}\cdot N_{k}^{e}E_{p_{k}}^{e}\right]dV}$ (21)

We can redefine ${K}_{ij}^{e}$ as follows:

$\displaystyle{K1}_{ij}^{e}=\iiint_{\Omega_{e}}{\left[\left(\nabla\times N_{i}^% {e}\right)\cdot\left(\nabla\times N_{j}^{e}\right)\right]dV}$ (22) $\displaystyle{K2}_{ij}^{e}=\iiint_{\Omega_{e}}{\left[N_{i}^{e}\cdot N_{j}^{e}% \right]dV}$ (23)

By synthesizing the finite element equations of all of the elements, we can obtain the general finite element equation:

$\displaystyle KE_{s}=b,$ (24)

Where $E_{s}$ is the secondary electric field:

$\displaystyle K=K1-i\omega\mu\sigma K2$ (25)

We then use the IDR(s) iterative algorithm to solve the linear equation, namely Eq. (24) [37], and the coefficient matrix is compressed and stored in CSR format.

4. Example

4.1 Proof of algorithm

To test the correctness of the algorithm, which is presented in this paper, we consider the design of a four-layer marine sediment model, whose parameters are given in Table 1. The fourth layer is composed of pyrite, hydrocarbon, water and sandstone, as shown in Fig. 4a. The unstructured mesh of the layer model is as shown in Fig. 4b. The A horizontal electric dipole along the X direction placed at 950 m under sea-surface is used as the excitation source. The frequency of the source is 0.1 Hz. The source current is 1 A. Receivers are located at 500: 200: 10000. Figure 5 shows the comparison between the numerical solution and quasi-analytical solution solved by the Hankel integral algorithm. We can observe that the numerical solution is in good agreement with the quasi-analytical solution, which validates the accuracy and validity of the proposed algorithm.

Table 1
The incremental parameters of marine layered medium model

Variable	Unites	Reservoir	Sediment	sea
${\sigma}$	s/m	${\sigma}_{e}$	1	3.3
${\sigma}_{py}$	s/m	15	–	–
${\sigma}_{qz}$	s/m	0.001	–	–
${\sigma}_{\textit{gas}}$	s/m	0.0001	–	–
${a}_{py}$	–	0.22	–	–
${a}_{qz}$	–	0.3	–	–
${a}_{\textit{gas}}$	–	0.2	–	–
${\Phi}$	%	0.05	–	–
Sw	%	0.5	–	–
Vpy	%	0.02	–	–

Figure 4.

Sketch of an Marine horizontal layered medium model. (a) Geometric sketch map of a reservoir model. (b) Mesh for a reservoir model at $y=$ 0 m. The green spot in this Fig. 4a indicates the excitation dipole source, the green rectangle is the reservoir.

Figure 5.

Comparison between numerical solution and quasi analytical solution of electric fields.

4.2 Example 2

To analyze the influence of different rock structure parameters on marine controlled source electromagnetic fields, we consider a four-phase medium (pyrite, water, hydrocarbon and quartz) reservoir model, and study the forward responses with varying structure parameters. The size of the reservoir is 5*5*1 km, with the center located at (4500, 0, 2500). The incremental model parameters of the marine reservoir model are shown in Table 2, and the geometric sketch is shown in Fig. 6a. The domain is discrete by using the unstructured mesh, as shown in Fig. 6b. We carry out local encryption in the vicinity of the source and lines. The excitation source is a horizontal electric dipole along the $x$ direction, located at ( $-$ 2000, 0, 950). The current is 1 A. Due to limited space, we simply set the frequency as 0.1 Hz. The receiver electrodes are located at $z=$ 1000 m. Next, the response characteristics of each component in the secondary field of $y=$ 0 m and $z=$ 1000 m are analyzed.

Table 2
The incremental parameters of four-phase reservoir model

Variable	Unites	Reservoir	Sediment	Sea
${\sigma}$	s/m	${\sigma}_{e}$	1	3.3
${\sigma}_{py}$	s/m	15	–	–
${\sigma}_{qz}$	s/m	0.001	–	–
${\sigma}_{\textit{gas}}$	s/m	0.0001	–	–
${a}_{py}$	–	0.22	–	–
${a}_{qz}$	–	0.3	–	–
${a}_{\textit{gas}}$	–	0.2	–	–
${\Phi}$	%	0.05 0.25 0.5	–	–
Sw	%	0.5	–	–
Vpy	%	0.02	–	–

Figure 6.

Sketch of an off-shore hydrocarbon reservoir model. (a) Geometric sketch map of a reservoir model. (b) Mesh for a reservoir model at $y=$ 0 m. The green spot in this Fig. 6a indicates the excitation dipole source, the back rectangle is the reservoir.

4.2.1 Influence of porosity on controlled source electromagnetic fields

To analyze the influence of various rock porosities on marine controlled source electromagnetic fields, we set up various rock porosity parameters of a hydrocarbon reservoir for forward calculation. The specific parameters are shown in Table 2.

Figure 7 shows the imaginary and real parts of the secondary electromagnetic fields with varying porosity. It can be seen from Fig. 7 that with increasing porosity, in the case of the same water saturation, the variation range of the imaginary and real components of the secondary electromagnetic fields decrease significantly.

4.2.2 Influence of pyrite conductivity on the controlled source electromagnetic field

To analyze the effects of different particle conductivities on the controlled source electromagnetic fields, we set up different particle conductivity parameters of the hydrocarbon reservoir for forward calculation. The conductivities ${\sigma}_{py}$ of the pyrite are 0.15, 1.5 and 15, respectively, the porosity ${\Phi}$ is 0.4, and the remaining parameters are shown in Table 2.

The plots of the real and imaginary parts of the secondary electromagnetic fields with different pyrite conductivities are shown in Fig. 8. It can be seen from the figure that, with the increasing of the pyrite conductivity, the anomalous amplitude of the imaginary components and real components of the secondary electromagnetic fields first reduce significantly, then the abnormal shape is reversed. Therefore, the effects of water-bearing hydrocarbon-bearing sandstones at low resistivity of pyrite on marine controlled source electromagnetic fields are greater than the situation at high resistivity of pyrite.

Figure 7.

Plots of the real and imaginary parts of the secondary electromagnetic fields with varying porosity.

Figure 8.

Plots of the real and imaginary parts of the secondary electromagnetic fields with varying pyrite conductivity.

Figure 9.

Plots of the real and imaginary parts of the secondary electromagnetic fields with varying pyrite volume fraction.

Figure 10.

Plots of the real and imaginary parts of the secondary electromagnetic fields with varying water saturation.

Figure 11.

Plots of the real and imaginary part of the secondary electromagnetic fields with different pyrite grain aspect ratio.

4.2.3 Influence of pyrite volume fraction on the controlled source electromagnetic fields

In order to analyze the effects of the various volume fraction of pyrite on the marine controlled source electromagnetic fields, we set up different volume fraction parameters of pyrite of hydrocarbon-bearing reservoirs for forward calculation. The volume fractions of pyrite $V_{py}$ are 0.02, 0.2 and 0.4, respectively. The remaining parameters are shown in Table 2.

The plots of the real and imaginary parts of the secondary electromagnetic fields with various volume fractions of pyrite are shown in Fig. 9. As can be seen from the figure, the changes of the real and imaginary components of the secondary electromagnetic fields with varying volume fractions of pyrite are similar with the case of generally increasing the conductivity of the pyrite, under the condition of the same volume fraction, i.e. abnormal amplitude decreasing, followed by the shape of abnormality reversing.

4.2.4 Influence of water saturation on controlled source electromagnetic fields

In order to analyze the effects of varying water saturation on the marine controlled source electromagnetic fields, we set up various water saturation parameters of hydrocarbon reservoirs for forward calculation. The water saturations Sw are 0.05, 0.4 and 0.8, respectively, the porosity $\Phi$ is 0.5, and the remaining parameters are shown in Table 2.

The plots of the real and imaginary parts of the secondary electromagnetic fields with different water saturations are shown in Fig. 10. As can be seen from the figure, in the case of the same porosity, with the increasing of water saturation, the abnormal amplitude of the imaginary and real components of the secondary electromagnetic fields decreases, and the variation range is wide.

4.2.5 Influence of particle aspect ratio on controlled source electromagnetic fields

In order to analyze the effects of different particle aspect ratios on the marine controlled source electromagnetic fields, we set up different particle aspect ratio parameters of hydrocarbon reservoirs for forward calculation. The particle aspect ratios of pyrite $\alpha_{py}$ are 0.03, 0.3 and 0.9, respectively the porosity ${\Phi=0.5}$ , and the water saturation Sw $=$ 0.5. The remaining parameters are shown in Table 2.

The plots of the real and imaginary parts of the secondary electromagnetic fields with different pyrite grains aspect ratio are shown in Fig. 11. As can be seen from the figure, with the increasing of the pyrite grains aspect ratio, the abnormal amplitude of the imaginary components and real components of the secondary electromagnetic fields decreases, and the variation range is relatively wide. However, compared with the porosity, water saturation, electrical conductivity and volume fraction of the particles, the influence of the particle aspect ratio on the electromagnetic fields is quite small.

5. Conclusion

In this paper, we use the increment model to calculate the effective conductivity of the multi-medium. Then we solve the 3D MCSEM modeling problem by using the vector finite element method, which is based on unstructured mesh with the secondary formulation. We analyze the influences of the parameters (porosity and water saturation) on the secondary fields of the controlled source electromagnetic fields. Below are some of the conclusions obtained.

Introducing the multi-phase incremental model to characterize electrical properties of the rocks is feasible and valid. It can provide a new way to further study the influences of the composition and structure of rocks on the conductivity.

In the case of certain porosity, when the water saturation, electric conductivity, volume fraction and particle aspect ratio increase, the variation amplitude of the secondary electromagnetic fields increases. Under the condition of certain water saturation, the larger the porosity of rocks is, the lower abnormal amplitude of secondary electromagnetic fields will be. Therefore, it is helpful to further validate the accuracy of data interpretation when the factors in the data interpretation are taken into consideration.

To gain a better understanding of the effects of porosity, water saturation and other parameters on MCSEM prospecting, the parameters are necessarily taken into consideration in the inversion process. Therefore, the 3D inversion of MCSEM based on the multi-phase incremental model will be completed in the future.

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Characteristics analysis of 3D marine CSEM response using the vector finite element method with secondary formulation

Abstract

Keywords

1. Introduction

2. Introduction of incremental model

2.1 Asami equation

3.1 Governing equation

4.1 Proof of algorithm

Table 1 The incremental parameters of marine layered medium model

Table 2 The incremental parameters of four-phase reservoir model

4.2.2 Influence of pyrite conductivity on the controlled source electromagnetic field

4.2.4 Influence of water saturation on controlled source electromagnetic fields

4.2.5 Influence of particle aspect ratio on controlled source electromagnetic fields

5. Conclusion

References

Table 1
The incremental parameters of marine layered medium model

Table 2
The incremental parameters of four-phase reservoir model