Method for saturation evaluation of a graphite-containing cheese root formation

Abstract

A method for evaluating the saturation of a kerogen-containing subterranean formation includes obtaining a conductivity value and a dielectric constant value for the formation, and providing an effective medium model that relates the conductivity and the dielectric constant to a water-filled porosity of the formation and an effective aspect ratio of graphite kerogen particles in the formation. The obtained conductivity value and the dielectric constant value are input into the model, which in turn is processed to calculate the water-filled porosity. The method can also optionally include evaluating the water-filled porosity to estimate a hydrocarbon yield of the formation.

Description

[0001] Cross-references to related applications

[0002] This application claims the benefit of U.S. Provisional Application Serial No. 62 / 926,908, filed October 28, 2019, entitled "Method for Saturation Evaluation of Highly Mature Kerogen Bearing Formations," the entire contents of which are incorporated herein by reference. Background Technology

[0003] Evaluating formation fluid saturation based on electromagnetic (EM) response (e.g., electromagnetic logging results) is the most common practice in oil reserve quantification. Typically, the formation resistivity (the reciprocal of conductivity) is measured and then interpreted along with saturation formulas to obtain formation water saturation. In the zero-order case, the formation EM response can be directly correlated with the amount of saturated brine in the formation, allowing the establishment of correlations between water saturation and conductivity signals, such as Archie's formula.

[0004] However, the presence of certain minerals has been shown to alter the EM response from Archie-type formations, for example, in the lower radio frequency range. A notable example includes shaly sand formations, where clay minerals contribute to both the electrical conductivity and dielectric constant signals. Various saturation formulas have been proposed to evaluate the water saturation of clay-bearing formations.

[0005] Another striking example includes mature kerogen formations (mature kerogen formations are generally understood to be formations containing graphite kerogen). It has been observed that as kerogen maturity increases, resistivity initially increases due to increased oil saturation, then reverses to very low resistivity values. Such low resistivity cannot be explained by Archie's formula or models that include clay effects. Therefore, conventional analysis cannot accurately determine the hydrocarbon potential of mature kerogen formations. Summary of the Invention

[0006] A method for evaluating the saturation of graphite kerogen formations is disclosed. The method includes obtaining the formation's electrical conductivity and dielectric constant values. An effective medium model is provided that correlates the electrical conductivity and dielectric constant with the formation's water-bearing porosity and the effective aspect ratio of the graphite kerogen grains in the formation. The electrical conductivity and dielectric constant values ​​(complex dielectric constant) are input into the effective medium model, which is then processed to calculate the formation's water-bearing porosity. This processing may further include calculating the effective aspect ratio of the graphite kerogen grains.

[0007] This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it used to limit the scope of the claimed subject matter. BRIEF DESCRIPTION OF DRAWINGS

[0008] For a more complete understanding of the disclosed subject matter and its advantages, reference is now made to the following description taken in conjunction with the accompanying drawings in which:

[0009] Figure 1 An example schematic diagram of a subsurface formation is depicted for generating the disclosed effective medium model.

[0010] Figure 2A and Figure 2B Plots of predicted permittivity (2A) and conductivity (2B) versus frequency are depicted for varying values of the ξ0parameter.

[0011] Figure 3A and Figure 3B Plots of predicted permittivity (3A) and conductivity (3B) versus frequency are depicted for varying values of the φ w parameter.

[0012] Figure 4A and Figure 4B Crossplots of conductivity versus permittivity as a function of the water-filled porosity parameter φ w (4A) and the aspect ratio parameter ξ0(4B) are depicted.

[0013] Figure 5A , 5B , 6A, 6B, 7A, and 7B depict crossplots of conductivity versus permittivity comparing model predictions and three field data examples.

[0014] Figure 8 A first schematic workflow is depicted.

[0015] Figure 9 A second schematic workflow is depicted.

[0016] Figure 10 A third schematic workflow is depicted.

[0017] Figure 11 A flowchart of one disclosed method embodiment is depicted. DETAILED DESCRIPTION

[0018] The disclosed embodiments generally relate to methods for evaluating the hydrocarbon-bearing potential of subterranean formations, and more particularly to methods for saturation evaluation of formations containing graphitic kerogen. Conductivity values and dielectric constant values (e.g., obtained from electromagnetic logging measurements) are input into an effective medium model, which is then processed (e.g., via inversion processing) to calculate the water-filled porosity of the formation. The model relates the conductivity and dielectric constant of the formation to the water-filled porosity of the formation and the effective aspect ratio of the graphitic kerogen particles in the formation, and is based (in part) on the polarizability response of the graphitic kerogen particles (particulates) dispersed in the formation. The model can also be used to calculate the effective aspect ratio of the graphitic kerogen particles.

[0019] Advantageously, the disclosed methods can provide improved petrophysical evaluation of kerogen-bearing formations. In particular, the disclosed embodiments are able to more accurately determine the water-filled porosity of formations containing graphitic kerogen, which in turn can provide more accurate evaluation of the hydrocarbon-bearing potential of such formations. The electromagnetic response of the formation (whether resistivity, dielectric constant, or both) is the most widely available logging signal used in oilfield operations for obtaining water-filled saturation evaluation. Thus, obtaining accurate saturation interpretation based on EM signals is important for reserve quantification (e.g., determining the yield of hydrocarbons). As noted above, for certain formation mineral compositions, this evaluation is difficult (or even impossible). As observed in practice, the presence of graphitic kerogen often results in formation resistivity that is abnormally low, which cannot be explained by any conventional resistivity saturation evaluation. In some embodiments, saturation of formations containing graphitic kerogen can be evaluated based on the electromagnetic response, which can demonstrate significant improvement in petrophysical evaluation and reserve quantification.

[0020] It has been observed that formations containing highly mature kerogen in the dry gas window can have very low resistivity, which cannot be explained using existing saturation formulas or models. In these relatively low porosity formations, the resistivity can be less than 0.2 ohm-m. When the resistivity values become this low, the traditional calculation of hydrocarbon saturation and in-place hydrocarbons becomes unreliable, and without further investigation, the formation is adjudged to be wet (e.g., water-saturated). Moreover, it has been found that when both the dielectric constant and the conductivity are high, the electromagnetic signal can be dominated by the effect of graphitic kerogen, which is electrically conductive and often has a low aspect ratio (indicative of flaky or lamellar particles).

[0021] A model has been developed and is disclosed herein to explain the observed conductivity and dielectric constant in graphite-rich kerogen formations. The disclosed effective medium model describes the conductivity and dielectric constant signals for formations containing water-wet graphite kerogen. The model includes a formulation for the polarization response of spherical conductive particles immersed in brine that not only accounts for the geometric and conductive effects of the particles independently, but also accounts for the interaction between them. In addition to the usual petrophysical parameters, such as the water phase tortuosity exponent, brine salinity, and water-filled porosity, the model can require input of the volume fraction, typical size (distribution), and phenomenological aspect ratio of the graphite kerogen. The conductivity and dielectric constant predicted by the model are consistent with the EM response of formations containing highly mature kerogen.

[0022] In field applications, the volume fraction of graphite kerogen can be obtained through advanced formation evaluation based on spectroscopy logging. Then, based on the water phase tortuosity exponent, brine salinity, and fixed size distribution of graphite kerogen, the formation water saturation and the phenomenological aspect ratio of graphite kerogen can be estimated based on the conductivity and dielectric constant signals at typical resistivity logging tool frequencies. Thus, the model can advantageously provide a basis for improved saturation interpretation of formations containing highly mature kerogen.

[0023] As noted above, the methods described herein can be advantageously used to evaluate the water saturation of formations containing highly mature kerogen. As known to those of ordinary skill, due to the low resistivity observed in these formations, conventional resistivity saturation evaluation methods based on the Archie saturation formula or the shaly sand saturation formula cannot provide reliable interpretation. These conventional methods typically overestimate the water saturation (and thus underestimate the recoverable hydrocarbons). In contrast, the disclosed methods utilize resistivity (conductivity) measurements and dielectric constant measurements made at a single logging tool frequency (e.g., at 10 skHz or 100 skHz, as described in more detail below) and utilize an effective medium model that accounts for the polarization effects of graphite kerogen immersed in brine to calculate the formation water saturation. The correlation between the conductivity and dielectric constant signals predicted and explained by the model advantageously provides a pathway for water saturation evaluation of formations containing highly mature kerogen where reliable saturation formulas did not previously exist.

[0024] The methods disclosed herein provide a model and associated workflow for water saturation of formations containing graphite kerogen. The methods use conductivity values and permittivity values from EM measurements of a formation, e.g., in a frequency range from about 10 kHz to about 200 kHz. The methods also utilize the volume fraction of graphite kerogen in the formation, which can be obtained, e.g., from nuclear logging measurements such as spectral gamma ray measurements. It should be understood that the disclosed embodiments are not limited to measurements by any particular type or kind of EM logging instrument, so long as both conductivity values and permittivity values can be determined from the measurements.

[0025] Turning now to Figure 1 , a schematic diagram (or representation) of a subsurface formation is depicted for modeling a subsurface formation of interest. The representation on the left side of the diagram schematically depicts a conventional bimodal formation model, in which the dielectric behavior of the formation is estimated by a bimodal distribution of spheres and spheroids. The representation on the right side of the diagram schematically depicts a formation model used to develop the disclosed methods, and includes graphite kerogen spheres distributed in the bimodal distribution of spheres and spheroids. The graphite kerogen is estimated by electrically conductive spheroid particles having large and small radii a and b (large radius is a, small radius is b) as shown.

[0026] The EM response of a formation containing highly mature (graphitic) kerogen can be better understood by first solving the polarization response of a single graphite particle (or spheroid) immersed in salt water. The particle is estimated by an electrically conductive spheroid as shown in Figure 1 , which accounts for both the geometry (aspect ratio of the spheroid) and the conduction effects of the spheroid.

[0027] The polarization coefficient of a graphite spheroid immersed in salt water is derived in this work. The derivation treats the graphite spheroid as a dielectric material having an electrical conductivity σ g and a relative permittivity ∈ g . The assumption is made that the potential inside the particle is governed by Laplace’s equation, i.e., there is no net free charge inside the conductive particle except at the boundary. This assumption implies that all (or, e.g., substantially all) of the electrons or holes that are created upon application of an external electric field are instantaneously accumulated at the boundary of the particle. In other words, the transient time for electrons or holes to move from the bulk to the boundary is much shorter than any time scale associated with the electromagnetic radiation frequencies used to make EM measurements.

[0028] The derivation of the polarization coefficient also assumes no exchange of ions and charges (e.g., via oxidation and / or reduction reactions) between the graphite particle (spheroid) and the salt water. This assumption leads to the accumulation of electrons / holes and anions / cations at the particle-liquid interface, which induces the creation of a double layer upon application of an external electric field that results in a strong polarization effect.

[0029] Graphite microparticles (modeled as flattened spheres immersed in salt water) parallel to the microparticles An electric field is applied to the long axis a of the particle and perpendicular to the particle. The polarization coefficient when an electric field is applied to the major axis a can be expressed mathematically, for example, as follows:

[0030]

[0031]

[0032] Where ε g =∈ g +iσ g / (ω∈0) is the complex permittivity of the graphite particles, ε g It is the relative permittivity, σ g It is the electrical conductivity of the particles, ε w =∈ w +iσ w / (ω∈0) is the complex permittivity of formation water (saltwater), ε w It is the relative permittivity, and σ w ω is the electrical conductivity of the salt water. As commonly used, ω is the radial frequency, and ∈0 is the vacuum permittivity.

[0033] Continuing with Equations 1a and 1b, the depolarization factor L is parallel to and perpendicular to the axis of symmetry (major axis a). p and L n Determined by (only) the shape of the graphite particles (e.g., aspect ratio b / a). For oblate spheroids, L n =(1-L) p ) / 2. This also facilitates the following definition of L. p =1-δ g , where δ g The further relationship with the geometric parameter ξ0 is as follows:

[0034]

[0035] in This is a Legendre function of the second kind. The geometric parameter ξ0 is the radius of the sphere in spherical coordinates and is related to the aspect ratio (the ratio of the minor axis to the major axis), as shown below: For sheet-like or layered particles where 0 < ξ0 << 1, ξ0 is approximately equal to the aspect ratio (i.e., ξ0 ≈ b / a).

[0036] Further referencing formulas 1a and 1b, τ D This is the characteristic time of ion dynamics in the electrolyte (salt water), and can be represented as follows:

[0037]

[0038] Where λ D is the Debye length, and D is the diffusion coefficient of ions in the salt water.

[0039] Furthermore, referring to formulas 1a and 1b, g p (hβ, ξ0) and g n (hβ, ξ0) is a function of the parallel polarization coefficient and the perpendicular polarization coefficient, ξ0 and hβ. Here, h is the half-distance between the two foci of the oblate spheroid, and β is the inverse decay length scale, defined as:

[0040]

[0041] In the case of the lowest nontrivial order, g in equation (1a) p The functional form of (hβ, ξ0) is given by the following equation:

[0042]

[0043] in

[0044]

[0045]

[0046] in It is a Legendre function of the first kind.

[0047] In the direction perpendicular to the axis of symmetry, the function g in formula 1b n (hβ, ξ0) is given by the following equation:

[0048]

[0049] in

[0050]

[0051]

[0052] in and These are the first and second types of Legendre functions, respectively.

[0053] The polarization coefficients given in Equations 1a and 1b approximate the polarization response of conductive particles (such as graphite kerogen) immersed in brine and explain the interaction between particle geometry and its conductivity. At the logging frequency (as described above), these coefficients enable the establishment of a more faithful model of the subsurface formation, which better captures the conductivity and dielectric constant responses of graphite kerogen-bearing formations for saturation interpretation.

[0054] The polarization coefficients given above (which describe the polarization response of graphite kerogen particles immersed in brine) are incorporated into the effective medium model to model the saturation response of formations containing mature graphite kerogen. For better understanding, the effective medium model can be considered to consist of two main components (or developed in two main steps). The first includes the conductivity response affected by conventional aqueous phase tortuosity and can be captured by a bimodal or Stroud-Milton-De (SMD) model or any other reasonable dielectric dispersion model that allows adjustment of the so-called cementation index. The second includes the EM response due to the presence of highly mature (graphite) kerogen particles, which can be captured by further mixing non-spherical (quasi-spherical) conductive particles into the dielectric background obtained in the first step. This results in a diluted mixture of graphite kerogen particles in the bimodal or SMD model. In the following discussion, the bimodal model is used in the first step to establish the dielectric background medium. In the second step, the graphite kerogen particles are incorporated into the bimodal model using the conventional Maxwell-Garnett mixing formula. Figure 1 The method is schematically depicted in the figure, where the left side of the figure depicts a bimodal model and the right side of the figure depicts a bimodal model with diluted inclusions containing spherical graphite kerogen particles.

[0055] The bimodal model aims to capture the so-called Maxwell-Wagner polarization caused by the texture effects of rock particles (Kenyon, Texture effects on megahertz dielectric properties of calcite rock samples, J. Applied Physics, 55(8) 3153-3159, 1984), and is commonly used to describe the dielectric dispersion of formations in the 10 MHz and 1 GHz frequency range. However, this bimodal model can be used at lower frequencies (e.g., induction logging and propagation logging frequencies), where the model includes a mixture of two types of rock particles (uncharged dielectric spheres with a single aspect ratio and uncharged dielectric flat spheres) entering the aqueous / saltwater phase. By constructing a differential effective medium approximation, the predicted dielectric response of the bimodal model is obtained as an implicit solution, with the following functional form:

[0056]

[0057] Where ε BM =∈ BM +iσ BM / (ω∈0) is the complex permittivity of the background medium predicted by the bimodal model, ∈ BM It is the relative permittivity, σ BM It is conductivity, and φ BMIt refers to the water-bearing porosity (in the bimodal model). i It is the extreme point, and p i It is the residual of the function 1 / (3εF(ε)), where F(ε) is the sum of the polarization coefficients of the mixed particles, which is weighted by their fractions and given by the following equation:

[0058]

[0059] Where p is the volume fraction of uncharged oblate spheroids in the rock matrix.

[0060] Further referring to Formula 10, having a dielectric constant ∈ m The polarization coefficient of the sphere (mixed into a lossy dielectric background with a complex permittivity ε) is given by the following equation:

[0061]

[0062] Similarly, for the bimodal model, and It is the polarization coefficient of an oblate spheroid mixed into a lossy dielectric background, wherein the applied electric fields are parallel and perpendicular to the axis of symmetry, respectively, and the polarization coefficient is given by the following equation:

[0063]

[0064] This is the depolarization factor of the sphere, as described above relative to Equation 2. Generally speaking, the modeled graphite particles and inert rock particles have different aspect ratios, making... (As also mentioned above relative to Formula 2) where δ BM This represents the geometric factor of the bimodal model.

[0065] One of the rock physics parameters provided by the bimodal model is the water phase tortuosity index (correlated with the Archie index under fully water saturation). This water phase tortuosity index sums the tortuosity contributions of spherical and oblate microparticles in the bimodal model and is given by the following equation:

[0066]

[0067] In the bimodal model, without spheres, i.e., when p = 0, the tortuosity index of the aqueous phase is greater than (e.g., always greater than) 3 / 2 (1.5). Since the tortuosity index of most strata in nature is in the range of 1.5 < w < 2.5, the bimodal model can be used to capture the pure texture effects of the conductivity and dielectric response to the background medium in the absence of graphite kerogen.

[0068] In the second step of establishing the effective dielectric model, graphite kerogen particles, represented by conductive oblate spheroids (as described above), are mixed into the aforementioned lossy dielectric background using a bimodal model. This is achieved by adding a volume fraction f of graphite kerogen. g The final water-bearing porosity becomes φ w =φ BM (1-f g The Maxwell-Garnet mixing formula for graphite kerogen particles added to the bimodal model background is given by the following equation:

[0069]

[0070] Where ε r =∈ r +iσ r / (ω∈0) is the complex permittivity of the rock (i.e., the strata containing graphite kerogen), ∈ r It is the relative permittivity, σ r is the electrical conductivity of the rock (strata), and the exponent i represents a group of particles with different sizes and aspect ratios. It should be understood that, as disclosed herein, ∈ r and σ r The measured dielectric constant and conductivity of the formation are represented (i.e., the inputs to the model, as described in more detail below).

[0071] To simplify the model, we can assume that the aspect ratio of graphite kerogen particles of different sizes is the same, i.e., a constant ξ0, and It is a discrete log-normal distribution, which can be represented by the following probability distribution function (PDF):

[0072]

[0073] It should be noted that the fractions of graphite kerogen particles of different sizes are logarithmically interleaved, where d = 2h represents the particle size, and μ and σ ln This represents the mean and variance of a log-normal distribution in the log-space.

[0074] In summary, the proposed effective medium model for complex conductivity is constrained by the following rock physics parameters: water-bearing porosity φ w The brine ε is determined given the formation temperature and pressure (T and P). w The complex conductivity of salt water salinity. w(Klein and Swift, An improved model for the dielectric constant of sea water at microwave frequencies, IEEE Transactions on Antennas and Propagation, 25(1), 104-111, 1977); and the water phase tortuosity index w. With p = 0.05 (i.e., 5% volume fraction of an uncharged oblate spheroid), w is defined by Equations 2 and 13 as the aspect ratio parameter ξ of the bimodal model. B The model is also subject to the following constraint: based on the graphite kerogen volume fraction f of the total formation volume. g The geometric parameters ξ0 of the graphite kerogen (approximately equal to the aspect ratio of the sheet-like or layered graphite kerogen particles as described above); and the mean μ and variance σ of the graphite kerogen size distribution. ln The following standard values ​​can also be input into the model: the relative permittivity of graphite kerogen ∈ g =10-15, Electrical conductivity σ of graphite kerogen g ≈10 5 S / m and the relative permittivity of the rock matrix ∈ BM =4.6-9. The exact values ​​of these material parameters are not as important to the modeled dielectric response as the larger polarization response due to the presence of graphite kerogen.

[0075] exist Figure 2A , 2B Examples of the dielectric constant and conductivity responses as functions of frequency, predicted by the model, are depicted in sections 3A and 3B. Figure 2A and Figure 2B In this study, the effect of aspect ratio on the dielectric constant and conductivity responses was demonstrated by varying the value of ξ0 while keeping the following parameters constant: water porosity φ. w =0.1, salinity 300 (ppm) (ppk), w≈1.96, μ=15, σ ln =3 and f g =0.03. It should be noted that smaller values ​​of ξ0 corresponding to more lamellar graphite kerogen particles produce stronger conductivity and dielectric constant responses at all the frequencies depicted.

[0076] exist Figure 3A and Figure 3B In the middle, the water-bearing porosity φ w The effect on the dielectric constant response and conductivity response is demonstrated by changing φ while keeping the following parameters constant. wValues: Aspect ratio ξ0 = 0.002, salinity (300 parts per thousand) (ppk), w ≈ 1.96, μ = 15, σ ln =3 and f g =0.03. As expected, formations with higher water-bearing porosity were shown to have stronger dielectric constant and conductivity responses (especially conductivity responses at all frequencies).

[0077] As is known to those skilled in the art, many EM logging instruments perform electromagnetic measurements at a single frequency and measure a complex voltage (with attenuation and phase transition characteristics), from which formation conductivity and dielectric constant can be determined. In some embodiments, it should be understood that since conventional EM measurements typically include only two data points measured at a single frequency (attenuation and phase transition or conductivity and dielectric constant), only two modeling parameters can be inferred from the measurement results. In the disclosed embodiments, the measured conductivity and dielectric constant values ​​are used to invert (i.e., solve) the aquifer porosity parameter φ. w The model with aspect ratio parameter ξ0. The remaining parameters described above are either fixed prior or used as input variables. For example, μ and σ of the size distribution. ln Appropriate values ​​can be determined through field calibration or a prior set of optimal values. Other rock physical parameters (such as brine salinity, aqueous tortuosity index w, temperature and pressure under downhole conditions, and the volume fraction of graphite kerogen f) g () is the input and can be obtained through measurement.

[0078] Figure 4A and Figure 4B The model's predicted porosity parameter φ at 20 kHz was described. w Cross plots of conductivity versus dielectric constant as a function of the aspect ratio parameter ξ0 (4A) and (4B). These plots illustrate the interaction between these two desired inversion parameters, where all other parameter values ​​are fixed. Different responses to these two parameters are observed. First, to achieve high conductivity and high dielectric constant in the formation, the model requires graphite kerogen grains to have a low aspect ratio (ξ0 << 1). Second, formation conductivity is shown as a function φ, which is larger than the formation dielectric constant. w Since these two parameters affect the EM response in drastically different ways, a stable interpretation of aquifer porosity based on conductivity and dielectric constant is expected.

[0079] Figure 5A , 5B Figures 6A, 6B, 7A, and 7B depict cross-plots of conductivity versus permittivity, comparing model predictions with three field data examples (using both field-available and reasonable modeling parameters). Field data (in...) Figure 5A ,6A (and 7A, indicated by square dots) represent wells from different US landmasses ( Figure 5A The first land well in the middle, Figure 6A The second land well and Figure 7A The average electrical conductivity and dielectric constant values ​​within the same formation type (the third land well in the study). Note that by changing φ... w The dielectric constant and conductivity values ​​obtained from the modeling with ξ0 fall within the range of average measurements from US land wells. Specifically, the water-bearing porosity φ used in the model... w Very close to the baseline water-bearing porosity from field data, without adjusting μ and σ values. ln This demonstrates the potential for saturation assessment based on dielectric constant and conductivity signals, as well as an effective medium model of graphite kerogen formations.

[0080] refer to Figure 5A and Figure 5B From available field information and interpretations, brine salinity, well temperature and pressure, and graphite volume fraction f were extracted. g ≈0.04 and the reference water-bearing porosity φ w，B ≈0.055. refer to Figure 6A and Figure 6B From available field information and interpretations, brine salinity, well temperature and pressure, and graphite volume fraction f were extracted. g ≈0.035 and the reference water-bearing porosity φ w，B ≈0.05. refer to Figure 7A and Figure 7B From available field information and interpretations, brine salinity, well temperature and pressure, and graphite volume fraction f were extracted. g ≈0.045 and the reference water-bearing porosity φ w，B ≈0.06.

[0081] Now go to Figure 8 to Figure 10 This describes other workflows (methods) for implementing the above model to determine the water saturation of mature graphite kerogen formations. For example... Figure 8 As described, in some implementations, the unknown φ can be obtained by directly solving (inverting) to obtain the dielectric constant and conductivity measured at the instrument frequency. w A model with parameters ξ0 is used to evaluate the water saturation of graphite kerogen formations. As shown in the figure, the model inputs consist of many inputs (left side of the figure). These inputs are then processed (e.g., via numerical inversion methods, such as minimizing a cost function) to calculate φ. w And ξ0 (as depicted on the right side of the figure).

[0082] Continue to refer to Figure 8The inputs include stratigraphic measurements and other prior known (or assumed) inputs (e.g., knowledge based on the field, stratigraphic type, or other information sources). As mentioned above, these other inputs may include μ and σ. ln These represent the mean and grain size variance of graphite kerogen in a log-normal distribution (e.g., as described above with respect to Equation 15). These other inputs may also include w, which represents the aqueous tortuosity index without graphite kerogen background (e.g., aqueous tortuosity of a background bimodal distribution as described above in more detail with respect to Equation 13). These other inputs may also include formation water salinity (i.e., salinity Sal). w The salinity of brine can be obtained, for example, from various measurements taken at the drilling site (known to ordinary technicians) or from prior knowledge of formation characteristics.

[0083] The model inputs can also be based on various logging measurements. For example, downhole temperature and pressure measurements are typically taken during drilling and / or logging operations. These temperature and pressure measurements can be averaged or otherwise processed to calculate the formation temperature result T and formation pressure value P, which are also input into the model. However, it should be understood that formation temperature and formation pressure measurements, as well as brine salinity, are not necessarily input into the effective medium model (e.g., the model described above relative to Equation 14). For example, temperature, pressure, and brine salinity values ​​can be input into another model (e.g., the water / brine dielectric model disclosed by Klein and Swift) to calculate the complex dielectric constant (ε) of the brine. w =∈ w +iσ w / (ω∈0) - includes the relative permittivity and conductivity of the salt water). This complex value (including permittivity and conductivity) can be input into the effective dielectric model.

[0084] The input for measurement may also include f g This represents the volume fraction of graphite kerogen in a kerogen-bearing formation. This parameter is typically in the range of about 1% to about 10%, but is not limited in this respect. The volume fraction of kerogen can be obtained from various sources, but can advantageously be obtained from nuclear logging measurements (e.g., spectroscopic gamma-ray logging measurements), from which the elemental distribution of the formation can be estimated. As known to those skilled in the art, the determined elemental distribution can be input into a conventional elements-to-minerals model to calculate the mineral composition of the formation, including the volume fraction of graphite kerogen (which is then input into an effective medium model). A suitable logging instrument for determining the volume fraction of graphite kerogen is available from Schlumberger Technology Corporation.

[0085] Continue to refer to Figure 8 The measurement inputs also include the complex permittivity ε of the formation. r Specifically, the inputs to the measurement also include ∈ r and σ r These represent the relative permittivity and conductivity of the subsurface formation (it should be understood that permittivity as referred to herein means only the permittivity). For example, these parameters can be obtained from various electromagnetic logging measurements, including cable induction logging measurements (e.g., at frequencies ranging from about 1 kHz to about 100 kHz) and logging-while-drilling propagation measurements (e.g., at frequencies ranging from about 100 kHz to about 2 MHz). Although the disclosed embodiments are explicitly not limited in this respect, EM measurements obtained at frequencies ranging from about 10 kHz to about 200 kHz (e.g., 20 kHz induction measurements or 100 kHz propagation measurements) can advantageously be used for φ. w And ξ0 provide the most accurate determination.

[0086] As will be readily understood by those skilled in the art, electromagnetic logging (EM) measurements are typically performed by deploying an electromagnetic measuring instrument with at least one transmitter (transmitting antenna) and at least one receiver (receiving antenna) in a subsurface wellbore penetrating graphite kerogen formation. For EM measurements, electromagnetic coupling is achieved by applying a time-varying current (alternating current) to the transmitting antenna to transfer electromagnetic energy into the surrounding environment (including the formation). This transferred energy generates a corresponding time-varying magnetic field in the local environment (e.g., instrument coupling, wellbore fluid, and formation). This magnetic field then induces currents (eddy currents) in the conductive formation. These eddy currents further generate secondary magnetic fields, which can produce a voltage response in the receiving antenna (e.g., by receiving the electromagnetic energy via measuring the complex voltage in the receiving antenna). The received energy (a complex voltage including both attenuation and phase transition components) can then be processed by calculating the dielectric constant and conductivity of the formation, for example, using conventional inversion algorithms.

[0087] Exemplary electromagnetic measurement instruments include cable induction instruments and logging-while-drilling propagation instruments. For example, instruments available from Schlumberger Technology Corporation can be used. or Electromagnetic measurements are performed using EM logging instruments. Of course, the disclosed implementation is not limited to using any particular EM logging instrument. As mentioned above, virtually any suitable measurement (or even estimate) of the dielectric constant and conductivity of graphite kerogen formations can be utilized.

[0088] Continue to refer to Figure 8After receiving various inputs (e.g., as shown on the left side of the figure), the effective medium model can be processed to calculate the water-bearing porosity φ. w And / or the effective aspect ratio ξ0 of graphite kerogen grains in the formation. Although the disclosed embodiments are not limited in this respect, the model (e.g., Formula 14) can be advantageously solved using an inversion algorithm that changes φ w and ξ0 parameters to make the calculated ∈ r and σ r Minimize the error between (e.g., using Equation 14) and the measured ∈ r and σ r Value (input value). This type of inversion technique is well known to those skilled in the art.

[0089] Figure 9 and Figure 10 An implementation scheme in which joint inversion is processed to calculate additional stratigraphic parameters is described. Figure 9 In the middle, the dielectric constant and conductivity of the formation, the temperature and pressure of the formation, and the above-mentioned... Figure 8 The additional inputs described are fed into the effective medium model depicted in the figure. As also mentioned above, it should be understood that temperature, pressure, and salinity can be input into the water / saltwater dielectric model to calculate the complex dielectric constant of the saltwater (which can be input into the model).

[0090] like Figure 9 Furthermore, the elemental distribution of the formation (e.g., obtained from nuclear logging measurements as described above) can be input into the depicted elemental model E. 模型，j (M i f g The element-to-mineral model aims to correlate the elemental distribution of a formation with the volume fraction M of minerals within that formation. i Volume fraction f of graphite kerogen g Related. Note that j represents various elements in the elemental distribution, and i represents various minerals in the strata.

[0091] Continue to refer to Figure 9 The effective medium model and elemental model are combined with the mineral model, for example, through joint inversion, to calculate the water-bearing porosity φ in the formation. w The effective aspect ratio ξ0 of graphite kerogen particles and the volume fraction f of graphite kerogen in the formation. g Volume fraction M of other minerals i For example, joint inversion can be handled by minimizing the following cost function:

[0092]

[0093] Where E jThe elemental composition of the strata is represented by W, which is a weighting factor (or function), and E. 模型，j (M i f g ) represents the relationship of mineral-to-element transformation (i.e., the above element-to-mineral model), and ∈ 模型 (φ w ,ξ0,f g ) and σ 模型 (φ w ,ξ0,f g ) represents the dielectric constant and conductivity predicted by the effective medium model given all the above modeling and rock physics parameters. σ ∈ and σ σ It is the standard deviation associated with each measurement.

[0094] Figure 10 The described implementation scheme is similar to Figure 9 The described implementation scheme, in addition to signal S j The input signal is compared with the depicted φ w M i and f g Associated rock physics model S 模型，j (φ w M i f g Besides these signals S j This can be generated, for example, from other logging measurements affected by mineral volume fraction and formation saturation, such as neutron, density, and / or gamma-ray measurements (e.g., as measured using triple combo logs available from Schlumberger Technology Corporation). As stated above regarding... Figure 9 The effective medium model and rock physics model are combined, for example, via joint inversion, to calculate the water-bearing porosity φ in the formation. w The effective aspect ratio of graphite kerogen ξ0 particles and the volume fraction f of graphite kerogen in the formation. g Volume fraction M of other minerals i For example, joint inversion can be handled by minimizing the following cost function:

[0095]

[0096] Where S j S represents various signals from additional logging measurements. 模型，j (φ w M i f g ) represents the rock physics model, Wj This represents the relative weights assigned to different signals j. This represents the standard deviation of the measured signal, and ∈ 模型 (φ w ,ξ0,f g ), σ 模型 (φ w ,ξ0,f g ), σ ∈ and σ σ As defined above regarding Formula 16.

[0097] Now go to Figure 11 A flowchart 100 depicts an exemplary implementation of a method for evaluating the saturation of graphite kerogen formations. The disclosed method includes obtaining formation electrical conductivity and dielectric constant values ​​at 102 (e.g., from electromagnetic logging measurements). At 104, an effective medium model is provided that correlates the provided electrical conductivity and dielectric constant values ​​with the formation's water-bearing porosity and the effective aspect ratio of the graphite kerogen grains. The obtained electrical conductivity and dielectric constant values ​​are input into the model at 106. The model is then processed at 108 (e.g., via inversion) to calculate the formation's water-bearing porosity.

[0098] Continue to refer to Figure 11 It should be understood that the treatment at 108 enables the calculation of both the formation's water-bearing porosity and the aspect ratio of the graphite kerogen grains. Furthermore, as depicted, the water-bearing porosity can optionally be further evaluated at 110 to estimate the formation's hydrocarbon yield. As is known to those skilled in the art, hydrocarbon yield is often a function of the total hydrocarbon reserves in the formation and the mobility of those reserves.

[0099] Further reference Figure 11 It should be understood that the conductivity and dielectric constant values ​​input into the model can be obtained from electromagnetic logging measurements (e.g., cable induction measurements and / or measurement-while-drilling propagation measurements). Such measurements can be inverted to calculate the conductivity and dielectric constant values ​​as described above (and as known to those skilled in the art). Although not explicitly stated in... Figure 11 In this process, the conductivity and dielectric constant values ​​can be obtained by deploying an electromagnetic measuring instrument in a wellbore that penetrates the formation, having the instrument transmitter emit electromagnetic energy into the formation, having the instrument receiver receive the emitted electromagnetic energy (e.g., an AC voltage signal), and processing the received electromagnetic energy to calculate the conductivity and dielectric constant values ​​of the formation.

[0100] Although not in Figure 11As described herein, it should be understood that 106 may also include: deploying a nuclear logging instrument in the wellbore, enabling the nuclear logging instrument to perform nuclear logging measurements (e.g., spectral gamma-ray measurements), processing the nuclear logging measurement results to estimate the volume fraction of graphite kerogen particles in the formation, and inputting the volume fraction of graphite kerogen particles in the formation into an effective medium model.

[0101] It should be understood that this disclosure includes many embodiments. These embodiments include, but are not limited to, the following embodiments and combinations thereof.

[0102] In a first embodiment, a method for evaluating the saturation of graphite kerogen formations is disclosed. The method includes: (a) obtaining electrical conductivity and dielectric constant values ​​for the graphite kerogen formation; (b) providing an effective medium model that correlates the electrical conductivity and dielectric constant with the formation's water porosity and the effective aspect ratio of the graphite kerogen particles in the formation; (c) inputting the electrical conductivity and dielectric constant values ​​obtained in (a) into the effective medium model provided in (b); and (d) processing the effective medium model to calculate the formation's water porosity.

[0103] The second implementation scheme may include the first implementation scheme, wherein (d) further includes: processing an effective medium model to calculate the water-bearing porosity of the formation and the effective aspect ratio of graphite kerogen particles in the formation.

[0104] The third implementation scheme may include either the first implementation scheme or the second implementation scheme, wherein (a) further includes: performing electromagnetic measurements of the formation; and processing the electromagnetic measurement results to calculate conductivity and dielectric constant values.

[0105] The fourth embodiment may include either the first embodiment or the second embodiment, wherein (a) further includes: deploying an electromagnetic measuring instrument having a transmitter and a receiver in an underground well that penetrates the formation; causing the transmitter to emit electromagnetic energy into the formation; causing the receiver to receive the emitted electromagnetic energy; and processing the received electromagnetic energy to calculate conductivity and dielectric constant values.

[0106] The fifth implementation scheme may include any of the first to fourth implementation schemes, and further includes: (e) evaluating the water-bearing porosity calculated in (d) to estimate the hydrocarbon yield of the formation.

[0107] The sixth implementation scheme may include any of the first to fifth implementation schemes, wherein the effective medium model also correlates the formation's electrical conductivity and dielectric constant with the formation's water porosity, the volume fraction of graphite kerogen particles in the formation, and the first and second polarization coefficients of the graphite kerogen particles.

[0108] The seventh embodiment may include the sixth embodiment, wherein the first polarization coefficient and the second polarization coefficient are at least related to the complex permittivity of the graphite kerogen grains, the complex permittivity of the formation water, and the aspect ratio parameter of the graphite kerogen grains, the first polarization coefficient being an electric field applied with respect to the axis of symmetry of the graphite kerogen grains, and the second polarization coefficient being an electric field applied with respect to the axis of symmetry of the graphite kerogen grains.

[0109] The eighth implementation may include any of the first to seventh implementations, wherein (c) further includes: inputting the volume fraction of graphite kerogen particles in the formation into the effective medium model provided in (b).

[0110] The ninth embodiment may include any of the first to eighth embodiments, wherein (c) further includes: deploying a nuclear logging instrument in a subsurface wellbore that penetrates the formation; enabling the nuclear logging instrument to perform nuclear logging measurements; processing the nuclear logging measurement results to estimate the volume fraction of graphite kerogen particles in the formation; and inputting the volume fraction of graphite kerogen particles in the formation into the effective medium model provided in (b).

[0111] The tenth implementation scheme may include any one of the first to ninth implementation schemes, wherein (c) further includes: inputting the temperature and pressure of the formation into the effective medium model.

[0112] The eleventh implementation may include any one of the first to tenth implementations, wherein (c) further includes inputting the following into the effective medium model: (i) the mean and variance of the log-normal distribution of the grain size of the graphite kerogen particles; (ii) the tortuosity index of the aqueous phase without graphite kerogen background; and (iii) the formation water salinity.

[0113] The twelfth embodiment may include any one of the first to eleventh embodiments, wherein (c) further includes: inputting the measured temperature of the formation, the measured pressure of the formation, and the salinity of the formation water into a water / saltwater dielectric model; processing the water / saltwater dielectric model to calculate the complex dielectric constant of the formation water, the complex dielectric constant including the dielectric constant and conductivity of the formation water; and inputting the calculated dielectric constant and conductivity of the formation water into an effective medium model.

[0114] The thirteenth embodiment may include any of the first to seventh and tenth to twelfth embodiments, wherein: (a) it further includes obtaining the elemental concentration of the formation from a nuclear logging instrument; (b) it further includes providing a mineral-to-element model that correlates the elemental concentration with the volume fraction of minerals in the formation; (c) it further includes inputting the elemental concentration obtained in (a) into the mineral-to-element model provided in (b); and (d) it includes processing the joint inversion of the effective medium model and the mineral-to-element model to calculate the following: (i) the water-bearing porosity of the formation; (ii) the effective aspect ratio of graphite kerogen grains in the formation; (iii) the volume fraction of graphite kerogen grains in the formation; and (iv) the volume fraction of other minerals in the formation.

[0115] The fourteenth implementation may include the thirteenth implementation, wherein (c) further includes inputting the following into the effective medium model: (i) the temperature and pressure of the formation; (ii) the mean and variance of the log-normal distribution of the grain size of the graphite kerogen particles; (iii) the tortuosity index of the aqueous phase without graphite kerogen background; and (iv) the formation water salinity.

[0116] The fifteenth embodiment may include any of the first to seventh and tenth to twelfth embodiments, wherein: (a) it further includes obtaining additional well logging results of the formation; (b) it further includes providing a rock physics model that correlates the additional well logging results with rock physics parameters of the formation, including the formation's water porosity and the volume fraction of minerals in the formation; (c) it further includes inputting the well logging results obtained in (a) into the well logging model provided in (b); and (d) it includes processing the joint inversion of the effective medium model and the rock physics model to calculate the following: (i) the formation's water porosity; (ii) the effective aspect ratio of graphite kerogen grains in the formation; (iii) the volume fraction of graphite kerogen grains in the formation; and (iv) the volume fraction of other minerals in the formation.

[0117] The sixteenth implementation may include the fifteenth implementation, wherein (c) further includes inputting the following into the effective medium model: (i) the temperature and pressure of the subsurface formation; (ii) the mean and variance of the log-normal distribution of the particle size of the graphite kerogen; (iii) the tortuosity index of the aqueous phase without graphite kerogen background; and (iv) the formation water salinity.

[0118] In the seventeenth embodiment, a method for evaluating the saturation of graphite kerogen formations is disclosed. The method includes: (a) providing an effective medium model that correlates the formation's electrical conductivity and dielectric constant with the formation's water-bearing porosity, the effective aspect ratio of graphite kerogen particles in the formation, and a first polarization coefficient and a second polarization coefficient of graphite kerogen particles in the formation brine; (b) performing electromagnetic logging measurements on the formation; (c) processing the electromagnetic measurement results to calculate the formation's electrical conductivity and dielectric constant; (d) performing spectral gamma-ray logging measurements on the formation; (e) processing the spectral gamma-ray logging results to estimate the volume fraction of graphite kerogen particles in the formation; and (f) performing spectral gamma-ray logging measurements on the formation... (g) Perform temperature and pressure measurements; (h) Combine the salinity of the formation brine with the temperature and pressure measurements to calculate the electrical conductivity and dielectric constant of the formation brine; (i) Input the following into the effective medium model: (i) the electrical conductivity and dielectric constant of the formation calculated in (c); (ii) the volume fraction of graphite kerogen particles estimated in (e); and (iii) the electrical conductivity and dielectric constant of the formation brine calculated in (g); and (i) process the effective medium model to calculate the water-bearing porosity of the formation and the effective aspect ratio of the graphite kerogen particles in the formation.

[0119] While methods for evaluating the saturation of graphite-bearing kerogen formations have been described in detail, it should be understood that various changes, substitutions, and modifications may be made herein without departing from the spirit and scope of this disclosure as defined by the appended claims. As will be understood by one of ordinary skill in the art as covered by embodiments of this disclosure, the figures, percentages, ratios, or other values ​​stated herein are intended to include such values, as well as other values ​​that are “about” or “approximately”. Therefore, the values ​​or terms such as “about,” “approximately,” “generally,” etc., should be interpreted broadly enough to include values, orientations, or characteristics that are at least sufficiently close to the stated value, orientation, or characteristic to perform the desired function or achieve the desired result.

[0120] It should be understood that references to “one embodiment” or “implementation” in this disclosure are not intended to exclude the existence of other embodiments that also incorporate the described features. For example, any element or feature described with respect to an embodiment herein may be combined with any element or feature of any other embodiment described herein. Therefore, all such modifications are intended to be included within the scope of this disclosure. Equivalent constructions including functional “device plus function” clauses are intended to cover structures described herein that perform the said function, including structural equivalents that operate in the same manner and equivalent structures that provide the same function. The applicant’s explicit intent is not to invoke any device plus function or other function claims against any claim, except for those in which the phrase “device for…” appears with the associated function.

Claims

1. A method for evaluating the saturation of graphite kerogen formations, the method comprising: (a) Obtain the electrical conductivity and dielectric constant values ​​of the graphite kerogen formation; (b) Provide an effective medium model that correlates the electrical conductivity and the dielectric constant with the water porosity of the formation and the effective aspect ratio of graphite kerogen particles in the formation; (c) Input the conductivity value and dielectric constant value obtained in (a) into the effective dielectric model provided in (b); (d) Process the effective medium model to calculate the water-bearing porosity of the formation; as well as (e) Evaluate the water-bearing porosity calculated in (d) to estimate the hydrocarbon yield of the formation.

2. The method of claim 1, wherein (d) further comprises processing the effective medium model to calculate the water-bearing porosity of the formation and the effective aspect ratio of the graphite kerogen particles in the formation.

3. The method according to claim 1, wherein (a) further comprises: (a1) Perform electromagnetic measurements on the strata; as well as (a2) Process the electromagnetic measurement results to calculate the conductivity value and the dielectric constant value.

4. The method of claim 1, wherein (a) further comprises: (a1) Deploy electromagnetic measuring instruments with transmitters and receivers in underground wells that penetrate the strata; (a2) The transmitter emits electromagnetic energy into the formation; (a3) Enable the receiver to receive the transmitted electromagnetic energy; as well as (a4) Process the received electromagnetic energy to calculate the conductivity value and the dielectric constant value.

5. The method of claim 1, wherein the effective medium model also correlates the electrical conductivity and dielectric constant of the formation with the water-bearing porosity of the formation, the volume fraction of the graphite kerogen particles in the formation, and the first polarization coefficient and the second polarization coefficient of the graphite kerogen particles.

6. The method of claim 5, wherein the first polarization coefficient and the second polarization coefficient are related to at least the complex permittivity of the graphite kerogen grains, the complex permittivity of the formation water, and the aspect ratio parameter of the graphite kerogen grains, wherein the first polarization coefficient is an electric field applied with respect to an axis of symmetry parallel to the graphite kerogen grains, and the second polarization coefficient is an electric field applied with respect to an axis of symmetry perpendicular to the graphite kerogen grains.

7. The method of claim 1, wherein (c) further comprises inputting the volume fraction of the graphite kerogen particles in the formation into the effective medium model provided in (b).

8. The method of claim 1, wherein (c) further comprises: (c1) Deploy nuclear logging instruments in an underground wellbore that penetrates the formation; (c2) Perform nuclear logging measurements using the nuclear logging instrument; (c3) Process nuclear logging measurements to estimate the volume fraction of graphite kerogen particles in the formation; as well as (c4) Input the volume fraction of the graphite kerogen particles in the formation into the effective medium model provided in (b).

9. The method of claim 1, wherein (c) further comprises inputting the temperature and pressure of the formation into the effective medium model.

10. The method of claim 1, wherein (c) further comprises inputting the following into the effective medium model: (i) the mean and variance of the log-normal distribution of the particle size of the graphite kerogen particles; (ii) the tortuosity index of the aqueous phase without graphite kerogen background; and (iii) the formation water salinity.

11. The method of claim 1, wherein (c) further comprises: The measured temperature, measured pressure, and salinity of the formation water are input into the water / saltwater dielectric model. The water / saltwater dielectric model is processed to calculate the complex dielectric constant of the formation water, the complex dielectric constant comprising the dielectric constant and conductivity of the formation water; and The calculated dielectric constant and conductivity of the formation water are input into the effective medium model.

12. The method according to claim 1, wherein: (a) also includes obtaining the elemental concentrations of the formation from nuclear logging instruments; (b) also includes providing a mineral-to-element model that correlates the concentration of the element with the volume fraction of minerals in the formation; (c) further includes inputting the elemental concentration obtained in (a) into the mineral-to-element model provided in (b); and (d) This includes a joint inversion of the effective medium model and the mineral-to-element model to calculate the following: (i) the water-bearing porosity of the formation; (ii) the effective aspect ratio of the graphite kerogen grains in the formation; (iii) the volume fraction of the graphite kerogen grains in the formation; and (iv) the volume fraction of other minerals in the formation.

13. The method of claim 12, wherein (c) further comprises inputting the following into the effective medium model: (i) the temperature and pressure of the formation; (ii) the mean and variance of the log-normal distribution of the grain size of the graphite kerogen particles; (iii) the tortuosity index of the aqueous phase without graphite kerogen background; and (iv) the formation water salinity.

14. The method according to claim 1, wherein: (a) also includes obtaining other well logging results of the formation; (b) It also includes providing a rock physical model that correlates the other well logging results with rock physical parameters of the formation, including the water porosity of the formation and the volume fraction of minerals in the formation; (c) also includes inputting the well logging results obtained in (a) into the well logging model provided in (b); as well as (d) This includes a joint inversion of the effective medium model and the rock physics model to calculate the following: (i) the water-bearing porosity of the formation; (ii) the effective aspect ratio of the graphite kerogen grains in the formation; (iii) the volume fraction of the graphite kerogen grains in the formation; and (iv) the volume fraction of other minerals in the formation.

15. The method of claim 14, wherein (c) further comprises inputting the following into the effective medium model: (i) the temperature and pressure of the formation; (ii) the mean and variance of the log-normal distribution of the grain size of the graphite kerogen particles; (iii) the tortuosity index of the aqueous phase without graphite kerogen background; and (iv) the formation water salinity.

16. A method for evaluating the saturation of graphite kerogen formations, the method comprising: (a) Provides an effective medium model that correlates the electrical conductivity and dielectric constant of a formation with the water porosity of the formation, the effective aspect ratio of graphite kerogen particles in the formation, and the first and second polarization coefficients of the graphite kerogen particles in the formation brine. (b) Perform electromagnetic logging measurements on the formation; (c) Process electromagnetic logging results to calculate the electrical conductivity and dielectric constant of the formation; (d) Perform spectral gamma-ray logging measurements on the formation; (e) Process the spectral gamma-ray logging results to estimate the volume fraction of the graphite kerogen particles in the formation; (f) Temperature and pressure measurements are performed on the formation; (g) Calculate the conductivity and dielectric constant of the formation brine by combining the salinity treatment temperature and pressure measurement results; (h) Input the following into the effective medium model: (i) the electrical conductivity and dielectric constant of the formation calculated in (c); (ii) The volume fraction of the graphite kerogen particles estimated in (e); and the electrical conductivity and dielectric constant of the formation brine calculated in (iii) and (g); (i) Process the effective medium model to calculate the water-bearing porosity of the formation and the effective aspect ratio of the graphite kerogen particles in the formation; as well as (e) Evaluate the water-bearing porosity calculated in (d) to estimate the hydrocarbon yield of the formation.

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