Aspects relate to water saturation in geological environments. More specifically, aspects relate to methods to estimate water saturation in electromagnetic measurements.
Conventional interpretation of electromagnetic measurements in heterogeneous materials neglects electrodiffusion and electrochemical effects occurring at interfaces. Such neglect of electrodiffusion and electrochemical effects may grow significant at the interfaces of, for example, geological stratum. As a result of this neglect, interpretations may be inaccurate, causing skewed results. For recovery of hydrocarbons, for example, such inaccuracies can seriously impact the economic viability of recovery of hydrocarbons from wellbores.
The following summary does not limit the overall scope of the application. In one non-limiting embodiment, a method to estimate water saturation in electromagnetic (EM) measurements is disclosed having making an electromagnetic measurement, performing at least one of creating an analytical forward model of the EM measurement, creating a numerical finite difference forward model of the EM measurement, performing an inversion, removing at least one petrophysically-adverse alteration of EM measurements in the frequency range from 1 Hz to 100 MHz and wherein the at least one petrophysically-adverse alteration is due to the presence of at least one of the following: pyrite, graphitic-precursors, magnetite, and other conductive minerals.
Other aspects and advantages of the claimed subject matter will be apparent from the following description and the appended claims.
It is proposed that effects of interfacial polarization on electromagnetic measurements in heterogeneous and anisotropic geological formations should be quantified in order to accurately estimate electrical properties of the host as well as the dispersed phase. Electromagnetic response of a porous geological material is affected by the presence of inclusions, vugs, veins, fractures, and thin-beds. In one non-limiting embodiment an analytical and numerical model of the interfacial polarization of a porous geological material containing dispersed phase to identify and quantify the interfacial polarization effects on complex conductivity response is disclosed. In the analytical model, a dipole moment is determined due to a single, isolated dispersed phase. Then a consistent effective medium formulation is used to determine effective complex conductivity of the geological mixture. Based on the prior knowledge of type of dispersed phase, an inversion algorithm is used to estimate the volume fraction of the dispersed phase and conductivity of the host medium or dispersed phase depending upon the requirement. Also, these models facilitate the used to understand the sensitivity of complex conductivity response to various electromagnetic petrophysical properties over a wideband frequency range (kHz-MHz). Petrophysical applications of the proposed invention may be used to: quantify the MIP effects of conductive mineral inclusions, such as pyrite and graphite, for improving resistivity interpretation of induction and dielectric measurements; quantify the MIP effects of conductive thin beds for improving resistivity interpretation of induction and dielectric measurements; quantify the MIP effects of conductive veins for improving resistivity interpretation of induction and dielectric measurements; quantify the MIP effects of parallel fractures for improving resistivity interpretation of induction and dielectric measurements; in conjunction with other petrophysical measurements, estimate volume fraction and the geometry of conductive minerals for applications in petrology, paleogeology, and paleothermometry; and/or improve resistivity interpretation in formations containing isolated vuggy porosity
One or more specific embodiments of the present disclosure are described below. These embodiments are merely examples of the presently disclosed techniques. Additionally, in an effort to provide a concise description of these embodiments, all features of an actual implementation may not be described in the specification. It should be appreciated that in the development of any such implementation, as in any engineering or design project, numerous implementation-specific decisions are made to achieve the developers' specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such development efforts might be complex and time consuming, but would nonetheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure.
When introducing elements of various embodiments of the present disclosure, the articles “a,” “an,” and “the” are intended to mean that there are one or more of the elements. The embodiments discussed below are intended to be examples that are illustrative in nature and should not be construed to mean that the specific embodiments described herein are necessarily preferential in nature. Additionally, it should be understood that references to “one embodiment” or “an embodiment” within the present disclosure are not to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features.
As defined herein, interfacial polarization refers to the external field-driven accumulation of charge carriers at the phase boundaries in geological mixtures. Dynamics of charge carriers (diffusion and electromigration) on both sides of the interface affects the electromagnetic (EM) response of the geological mixture. Pyrite-bearing sedimentary rocks and graphite-bearing thermogenic source rocks demonstrate MIP phenomena in an external electric field. A mechanistic model of interfacial polarization in geological mixture has been developed, as a non-limiting embodiment, based on Poisson-Nernst-Planck (PNP) equations for dilute solution in a weak electrical field. PNP equations are more realistic compared to circuit models that reduce transport problems of electrokinetics to electrostatic problem based on the assumption that the bulk concentration remains uniform at all times. The relationship of characteristic frequency of the dispersion curve is investigated and of static relative permittivity of the geological mixture to the dimensions, electrical properties, and volume fraction of the individual elements of the dispersed phase. Contrary to conventional literature, a strong dependence of complex conductivity response of a geological mixture has been found to the conductivity of the host medium.
Analytical Model
Modeling of interfacial polarization can be done using circuit models, empirical models, phenomenological models, or mechanistic models. A physically consistent model must satisfy Kronig-Kramers relationship. Many analytical models are built for cases when dispersed phase don't interact with each other. As a result, a single element is analyzed followed by applying an effective medium formulation to the entire mixture. An interfacial polarization mechanism has been modeled as a diffusion of counterions moving along the surface of the particle. This modeling framework neglects all bulk diffusion effects by calculating the potential outside the counterion layer as a solution to laplace equation rather than poisson's equation. Another approach to this problem is based on the concept of a diffused double layer. Non-linearity of this equation leads to extreme mathematical complexity which does not provide analytical expressions for relaxation parameters. A simplified model was developed which leads to an analytical solution for interfacial polarization for charged spherical particles in electrolyte solution. Another approach to analyze the effects of interfacial polarization in various hydrocarbon-bearing geological formations has been developed. In an external field, the charge carriers in the dispersed phase migrate and accumulate at the impermeable interface. Consequently, the dispersed phase behaves as dipoles in presence of electric field. Additionally, the charge carriers in the host medium migrate under the influence of external electric field and accumulate on the interface resulting in substantial dielectric enhancement. Taylor-series simplification is not applied to the effective medium formulation in order to account for the large reflection coefficient or dipolar coefficient that develops due to the interfacial polarization.
Numerical modeling work on dielectric enhancement and conductivity dispersion was not found relevant due to interfacial polarization. Inversion algorithm coupled to an analytical modeling was not found relevant.
The aim of this model is to describe the complex conductivity response of host medium, representing a porous geological material, containing small volume fraction of conductive phase, which can be a inclusion, vug, vein, fracture, or beds. Configurations are represented in
PNP Model Formulation
At t<0, no external voltage is applied, it is assumed there is no spontaneous accumulation of charges on the interface.
Under weak field approximation, such that |cj±|≤N0j±, an external electric field E=E0e−jwt results in perturbation of ionic charge densities and potentials near the interface from its equilibrium condition:
Nj±=N0j+cj±(r)e−jwt cos(θ)
Subscript for host medium=s
Subscript for dispersed medium=i
r is the distance along the normal to the interface.
θ is the angle between incident electric field and the normal to the interface.
cj± is the ion density variation due to electric field near the interface.
Charge carrier density in the medium, j, without an external field=N0j±
Mobility of charge carrier in the medium, j=μj±
Charge number of charge carrier in the medium, j=Zj±
The simplified assumption is that both of the media are binary and symmetric with respect to charge carrier:
Zj±=1; μs+=μs−=μs; μi+=μi−=μi; N0i+=N0i−=N0i; N0s+=N0s−=N0s
Conductivity of the medium, j=σj=2N0jμje
Complex conductivity of the medium, j=Kj=σj+iωεj
Continuity equation for charge carrier density based on mass conservation for each type of charge carriers,
Adding both the equations mentioned in 1 gives
ieωdj=∇(Jj++Jj−)=2e2N0jμjdj/εjeDjdj
where σj=2N0jμje and εj=εrjε0; Dj=μjkT/e
In equation 2,
Current density of each charge carrier type in each medium is a sum of current density due to drift current and diffusion current. Also, there is no generation/recombination reactions. Then, the transport equation representing conservation laws for ionic species can be written as—
Jj±=Jj,drift±+Jj,diffusion±=eNj±μjĒj eDj∇Ntj±=eNj±μj∇φjeDj∇Nj±
Where φj is electric potential and Ēj=∇φj
Diffusivity of charge carrier in medium, j=Dj=μjkT/e
where k is the Boltzmann's constant and T is absolute temperature
This gives Nernst-Planck equation
Distribution of charges within a medium leads to an electric potential,
φj(r,θ,t)=φj(r)e−jwt cos(θ)
Using Gauss's law, ∇(εj Ēj)=ρf,j=e(Nj+Nj−)=e(cj+cj−)
∇(εjĒj)=∇(εj∇φj)=εjφj
dj=(cj+cj−)
φj=edj/εj 5
Equation 3, 4, and 5 together are called the PNP equations.
Combining equation 5 and 2
Boundary Conditions
The interface is ideally polarizable or completely blocking without any faradic processes, so fluxes of charge carrier vanish on both sides of the interface, respectively.
BC1—Electric potential must be continuous at the interface assuming a zero intrinsic capacitance of interface. This capacitance may represent a stern layer of polarized solvent molecules and/or dielectric coating on the interface.
BC2—The normal component of the displacement component must be continuous at the interfaces. This corresponds to the fact that when diffusive effects are considered no surface charge distribution can occur.
BC3—The normal component of the current density must vanish at the interface. This condition expresses the fact that since no surface charge distribution can buildup, diffusive and electromigrative currents must cancel each other at the interface. Ideally polarizable or completely blocking interfaces without faradic processes are considered, so ionic fluxes have to vanish on the interface.
Effective Medium Formulations
where K{circumflex over (n)},eff is effective complex conductivity of the geological mixture.
L{circumflex over (n)} is the depolarization factor based on the shape of the dispersed phase.
{circumflex over (n)} is the direction of electrical measurement.
For thin beds and induced fractures:
For cylindrical veins and natural fractures:
For spherical inclusions and vugs:
Numerical Model
A numerical model was developed using COMSOL AC/DC module to simulate the effect of interfacial polarization due to randomly distributed dispersed phase in a host medium.
Inversion Algorithm
An inversion scheme based on Gauss-Newton minimization was developed for the purposes of estimating volume fraction of conductive mineral inclusions, such as pyrite and graphite, for paleothermometry and improving resistivity interpretation; estimating volume fraction of conductive thin beds for improving resistivity interpretation of induction and dielectric measurements; estimating volume fraction of conductive veins for improving resistivity interpretation of induction and dielectric measurements; estimating volume fraction of parallel fractures for improving resistivity interpretation of induction and dielectric measurements, and to diagnose fracture density; estimating volume fraction of isolated vuggy porosity for improving resistivity interpretation.
A first case is shown in
A second case is shown in
While the claimed subject matter has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this disclosure, will appreciate that other embodiments can be devised which do not depart from the scope of the claimed subject matter as disclosed herein. Accordingly, the scope of the claimed subject matter should be limited only by the attached claims.
The present application claims priority to U.S. Provisional Application 62/154,944 filed Apr. 30, 2015, the entirety of which is incorporated by reference.
Filing Document | Filing Date | Country | Kind |
---|---|---|---|
PCT/US2016/029993 | 4/29/2016 | WO | 00 |
Publishing Document | Publishing Date | Country | Kind |
---|---|---|---|
WO2016/176541 | 11/3/2016 | WO | A |
Number | Name | Date | Kind |
---|---|---|---|
20040164735 | Hurlimann et al. | Aug 2004 | A1 |
20060085135 | Clavaud | Apr 2006 | A1 |
20060136135 | Little | Jun 2006 | A1 |
20100017132 | Glinisky et al. | Jan 2010 | A1 |
20100185393 | Liang | Jul 2010 | A1 |
20100185422 | Hoversten | Jul 2010 | A1 |
20120293179 | Colombo | Nov 2012 | A1 |
20130241561 | Allen | Sep 2013 | A1 |
Number | Date | Country |
---|---|---|
103149220 | Jun 2013 | CN |
2282178 | Aug 2006 | RU |
WO2014000758 | Jan 2014 | WO |
WO2014165478 | Oct 2014 | WO |
2016081669 | May 2016 | WO |
Entry |
---|
International Search Report and Written Opinion issued in International Patent application PCT/US2016/029993, dated Sep. 1, 2016. 11 pages. |
Schwarz, Gerhard. A theory of the low-frequency dielectric dispersion of colloidal particles in electrolyte solutionl, 2. The Journal of Physical Chemistry,66(12), 2636-2642. 1962. |
Dukhin et al., Dielectric Phenomena and Double Layer in Disperse Systems and Polyelectrolytes. Journal of the Electrochemical Society, 121(4), 154C-154C. 1974. |
Grosse et al., Permittivity of a suspension of charged spherical particles in electrolyte solution. Journal of Physical Chemistry,91(11), 3073-3076. 1987. |
Grosse et al., The influence of diffusion on the dielectric properties of suspensions of conductive spherical particles in an electrolyte. Journal of Physics D: Applied Physics, 25(3), 508. 1992. |
Wong, J., An electrochemical model of the induced-polarization phenomenon in disseminated sulfide ores. Geophysics, 44(7), 1245-1265. 1979. |
Chu et al., Nonlinear electrochemical relaxation around conductors. Physical Review E, 74(1), 011501. 2006. |
Schmuck et al., Homogenization of the Poisson-Nernst-Planck equations for ion transport in charged porous media. arXlv preprint arXiv:1202.1916. 2012. |
Anderson et al., Identifying Potential Gas-Producing Shales From Large Dielectric Permittivities Measured by Induction Quadrature Signals, SPWLA 49th Annual Logging Symposium held in Edinburgh, Scotland, May 25-28, 2008, 10 pages. |
Misra et al., Interfacial polarization of disseminated conductive minerals in absence of redox-active species—Part 1: Mechanistic model and validation, Geophysics, vol. 81, No. 2, Mar. 1, 2016, pp. E139-E157. |
Wang et al., The Broadband Electromagnetic Dispersion Logging Data in a Gas Shale Formation: A Case Study, SPWLA 54 th Annual Logging Symposium, Jun. 22, 2013, 12 pages. |
Anderson et al., Observations of Large Dielectric Effects on Induction Logs, or Can Source Rocks Be Detected with Induction Measurements, 47th Annual Logging Symposium held in Veracruz, Mexico, Jun. 4-7, 2006, 12 pages. |
Number | Date | Country | |
---|---|---|---|
20180113088 A1 | Apr 2018 | US |
Number | Date | Country | |
---|---|---|---|
62154944 | Apr 2015 | US |