RU2279106C1 - Method for geo-electro-surveying with focusing of electric current (variants) - Google Patents

Abstract

FIELD: geophysical research, possible use for finding and contouring oil-gas deposits.

SUBSTANCE: method includes excitation of electromagnetic field within thick portion of researched environment, by letting through it a periodical series of rectangular current pulses with pauses between each one of them serially from two dipole sources. Between current pulses in pauses along whole length of these, momentary values of first and second axial and second orthogonal potentials differences are measured when resulting first difference of potentials between extreme measuring grounding parts is equal to zero. Along whole duration of each pause two momentary values positioned adjacently in time of first and second differences of potentials are selected, determining differences between their values. From values of differences, three normalized electrical parameters are calculated. Reverse problem is solved on basis of differential fading wave equation of mathematical physics for strength of dipole source in electrochemically self-polarizing conductive environment. Model of environment, most close to geometrical structure and electrical parameters of researched environment, is determined, and temporal cuts are constructed by electric conductivity, coefficient of caused polarization and time of fading of difference of potentials of aforementioned caused polarization.

EFFECT: increased success coefficient of searches for oil-gas deposits.

2 cl, 4 dwg, 1 tbl

Description

The invention relates to the field of geophysical research, and more particularly to ground-based geoelectro-prospecting methods using controlled artificial sources of electromagnetic fields with electric current focusing, they are designed to search and outline oil and gas deposits based on the separate determination and mapping of the thickness of sedimentary deposits characteristic of each element (horizon) rocks of the following three electrophysical parameters necessary to solve the problem, specific electrical conductivity caused by polarization and the decay time constant of the potential difference caused by polarization.

Known methods of geoelectrical exploration with artificial excitation of the medium under study by electric current (methods of resistance to direct and alternating current), which are designed to determine only one electrophysical parameter from the above three, namely electrical resistance, which is not enough to search and outline the oil and gas deposits. Among these methods, the most common is the pulsed method with alternating low-frequency current - the method of formation of the electric field.

Based on the results of field measurements, this method calculates the electrical resistance ρ _τ using the universal formula

where J is the measured current jump in the current dipole;

;ΔU is the measured voltage at the ends of the receiving ground MN or at the terminals of the horizontal ungrounded circuit, with which the rate of change of the vertical magnetic field is recorded

;

K is the geometric coefficient of the sounding installation (see "Electrical exploration", Handbook of geophysics. Ed. A.G. Tarkhov, M., Nedra, 1980, p.237) [1].

With this approach, which is usually used with all traditional methods of determining electrical resistance in geoelectrical prospecting with a controlled artificial current source, only summary information is obtained about all the structural elements of the medium under study, in which the field develops, since the distribution in the space of the measured current J of the source is nothing it is not controlled and there is no information about the indicated distribution in real-life three-dimensionally inhomogeneous media. This means that the normalization of the measured electric parameter ΔU according to the power supply current J of the source without focusing the current in three-dimensionally inhomogeneous media is pointless, since the current J does not carry any information about the medium being studied, but only information about the power of the current generator and the grounding resistance of the current electrodes of a current dipole.

Thus, resistance methods are not very suitable for searching and outlining oil and gas deposits, for at least two reasons: first, only one of the three electrophysical parameters of the medium under study is recorded for this purpose; the second is the recorded parameter for the same purpose is too coarse, because due to the lack of focusing of the current, the resistance of the volume of all geological objects of the medium under study, in which the electric field of the current source develops, is recorded in it.

Known methods of geoelectrical exploration, which use the effect of induced polarization inherent in sedimentary rocks and having anomalous values in environments in which oil and gas deposits are located, for example, the INFAZ-VP method (A.V. Kulikov, E.A. Shemyakin. Phase electrical exploration the method of induced polarization. M., Nauka, 1978, p.81-88) [2]. When using this method, φ _VP acts as an interpreted parameter - the phase shift between the voltage of the source and receiver, calculated for the entire sedimentary cover. Its layered definition is not performed. With this approach, the oil and gas reservoir is detected in the form of an integral anomaly in φ of the _airspace . This creates a false impression that the reservoir is displayed in _φv indirectly due to the halo dispersion of hydrocarbons in the “column” of overlying rocks, including near-surface ones. The method has another significant drawback, namely, the parameter recorded by it is significantly susceptible to distorting influence of electrical resistance.

Closest to the proposed is the method of geoelectrical exploration (N.I. Rykhlinsky et al. Method of geoelectrical exploration. Patent No. 1436675 by application No. 04216994 / (051440) of 03/31/87) [3], in which the medium under investigation is excited by a periodic sequence of rectangular current pulses passed through a grounded supply line (grounded dipole electrical source), and measure the first and second axial potential differences at the observation points in the pauses between current pulses, from which the mapped parameter is already formed based on normalization of uninformative for general supply current dipole source, and a first potential difference is proportional to the current density in the world under the point of measurement of this difference (the prototype).

The first disadvantage of this method is that due to the lack of focusing of the electric current, it is subject to the distorting effect of surface geological heterogeneities on the measurement results in three-dimensionally inhomogeneous media.

The second disadvantage of this method, despite its increased resolution when differentiating the geological section, is that it is not possible to completely separate the inherent elements of the geological environment, including the oil and gas deposits located in it, caused by polarization from transient electrodynamic processes associated with electrical conductivity the indicated elements of the strata composing the section of geological rocks.

The proposed method solves the problem of detection, contouring of oil and gas deposits. The technical result consists in providing the possibility of separating the parameters of electrical conductivity and induced polarization, as well as the possibility of determining the decay time constant of the potential difference caused by polarization - an important third along with the first two parameters.

The specified technical result is achieved by the fact that in the method of geoelectrical exploration, in which the electromagnetic field is excited along the axis of the sounding profile in the thickness of the medium under investigation, passing through it a periodic sequence of rectangular current pulses with pauses after each of them using a dipole electric source, and in each period of this the sequences at the sensing points measure the first and second axial differences of electric potentials and the second difference of electric potentials in the direction perpendicular to the axis of the profile, according to the invention, an electromagnetic field is excited along the axis of the sounding profile in the thickness of the medium under investigation, passing through it a periodic sequence of rectangular current pulses with pauses after each of them alternately from two dipole electrical sources, in each pause between current pulses throughout the entire time the existence of this pause at discrete time points with a constant time interval measure the sequence of instantaneous values of the first and second axial sequence of instantaneous values of the second differences of electric potentials in the direction perpendicular to the axis of the profile, at the same time at the same discrete time points in each pause between current pulses throughout the entire lifetime of this pause, while providing focusing of the current to eliminate the axial component of the current under the sensing point, maintaining equality zero of the resulting potential difference between the extreme measuring grounding, from the values of the measured differences of the electric potentials, three sets of normalized electrical parameters of dipole sources of normalized electrical parameters are calculated:

where k (t _i ) is the coefficient obtained from the equation ΔU _x (t _i ) ₁ + k (t _i ) ΔU _x (t _i ) 2 = 0;

Δt is the time interval between the two nearest measured instantaneous values of the first and second differences of electric potentials throughout the existence of a pause;

ΔU _x (t _i ) ₁ , ΔU _x (t _i ) ₂ Δ ² U _x (t _i ) ₁ , Δ ² U _x (t _i ) ₂ - instantaneous values of the first and second axial differences of electric potentials, measured in pauses of current on throughout the existence of each of these pauses from its beginning to the end at predetermined equal time intervals Δt, when currents are supplied to the first and second dipole electric sources, respectively;

Δ ² U _y (t _i ) ₁ , Δ ² U _y (t _i ) ₂ - instantaneous values of the second axial differences of electric potentials, measured in the direction perpendicular to the axis of the profile, in the pauses of current throughout the existence of each of these pauses from it beginning to the end at equal time intervals Δt when applying currents to the first and second dipole electric sources, respectively;

Δ ² U _x (t _i , Δt) ₁ , Δ ² U _x (t _i , Δt) are the differences between the separated time intervals M, the two nearest instantaneous values of the second axial differences of electric potentials, measured in pauses of current throughout the existence of each from these pauses;

using the values of normalized parameters and the differential equation of mathematical physics for the electric field strength of a dipole source in an electrochemically polarized conducting medium

- оператор Лапласа;Where

- Laplace operator;

- напряженность электрического поля дипольного источника, выраженная в уравнении для случая гармонического изменения величины электрического поля по времени;

- the electric field strength of the dipole source, expressed in the equation for the case of a harmonic change in the magnitude of the electric field over time;

σ (iωσ ₀ ητ) is the frequency-dependent electrical conductivity of the elements of the medium;

σ ₀ is the electrical conductivity of the elements of the medium without taking into account the effect of induced polarization;

η is the coefficient of their induced polarization;

τ is the decay time constant of the potential difference caused by polarization,

they solve the mathematical inverse problem, determine three electrophysical parameters inherent in each element of the medium: electrical conductivity σ ₀ , induced polarization η, and decay time constant of the potential difference caused by polarization, and construct three time sections from these parameters.

The achievement of the technical result is also provided by the second variant of the method of geoelectrical exploration, in which an electromagnetic field is excited along the axis of the sounding profile in the thickness of the medium under investigation, passing through it a periodic sequence of rectangular current pulses with pauses after each of them alternately from two dipole electrical sources, in each pause between pulses current for the entire duration of the existence of this pause at discrete time points with a constant time interval is measured after ovatelnost instantaneous values of the first and second axial electrical potential differences, while providing focusing current component to exclude the axial current under the sensing point while maintaining the vanishing of the resultant potential difference between the outer measuring earths; Three sets of independent dipole sources of normalized electrical parameters are calculated from the values of the measured differences in electric potentials:

where k (t _i ) is the coefficient obtained from the equation ΔU _x (t _i ) ₁ + k (t _i ) ΔU _x (t _i ) ₂ = 0;

Δt is the time interval between the two nearest measured instantaneous values of the first and second differences of electric potentials throughout the existence of a pause;

ΔU _x (t _i ) ₁ , ΔU _x (t _i ) ₂ Δ ² U _x (t _i ) ₁ , Δ ² U _x (t _i ) ₂ - instantaneous values of the first and second axial differences of electric potentials, measured in pauses of current on throughout the existence of each of these pauses from its beginning to the end at predetermined equal time intervals Δt, when currents are supplied to the first and second dipole electric sources, respectively;

ΔU _x (t _i , Δt), ΔU _x (t _i , Δt) ₂ , Δ ² U _x (t _i , Δt) ₁ , Δ ² U _x (t _i , Δt) ₂ - differences between the separated time interval Δt the two closest instantaneous values of the first and second axial differences of electric potentials, measured in pauses of current throughout the existence of each of these pauses;

using the values of normalized parameters and the differential equation of mathematical physics for the electric field strength of a dipole source in an electrochemically polarized conducting medium

- оператор Лапласа;Where

- Laplace operator;

- напряженность электрического поля дипольного источника, выраженная в уравнении для случая гармонического изменения величины электрического поля по времени;

- the electric field strength of the dipole source, expressed in the equation for the case of a harmonic change in the magnitude of the electric field over time;

σ (iωσ ₀ ητ) is the frequency-dependent electrical conductivity of the elements of the medium;

σ ₀ is the electrical conductivity of the elements of the medium without taking into account the effect of induced polarization;

η is the coefficient of their induced polarization;

τ is the decay time constant of the potential difference caused by polarization;

they solve the mathematical inverse problem, determine three electrophysical parameters inherent in each element of the medium: electrical conductivity σ ₀ , induced polarization η, and decay time constant of the potential difference caused by polarization, and construct three time sections from these parameters.

The invention is illustrated by drawings.

In FIG. 1 is a block diagram of a device for implementing the proposed method using a sensor of the first and second axial differences of electric potentials and a sensor of the second difference of electric potentials in a direction perpendicular to the axis of the profile.

Figure 2 shows the shape of the pulses as a function of time t: (a) the shape of one of a series of periodic rectangular pulses of current J in the network of the dipole source AB, (b) the shape of one of the pulses of the first and second potential differences.

; б - форма электрического поля в пределах измерительных заземлений M₁M₂ при сфокусированном токе при помощи токовых диполей B₁A₁ и А₂B₂; в - форма электрического поля в пределах измерительных заземлений M₁M₂ при возбуждении исследуемой среды при помощи одного токового диполя B₁A₁ без фокусировки тока; г - форма электрического поля в пределах измерительных заземлений M₁M₂ при возбуждении исследуемой среды при помощи одного токового диполя А₂В₂ без фокусировки тока.Figure 3 shows the shape of the electric field in a homogeneous medium: a - the shape of the propagation of current lines when focusing the current by maintaining a potential difference equal to zero

; b - the shape of the electric field within the measuring grounding M ₁ M ₂ with a focused current using current dipoles B ₁ A ₁ and A ₂ B ₂ ; in - the shape of the electric field within the measuring grounding M ₁ M ₂ when the studied medium is excited with the help of one current dipole B ₁ A ₁ without focusing the current; g is the shape of the electric field within the measuring earths M ₁ M ₂ when the medium under investigation is excited with the help of a single current dipole A ₂ V ₂ without focusing the current.

In FIG. 4 shows the results of mathematical modeling by the proposed method for a five-layer model of a medium with subhorizontal infinitely extended interfaces.

The device (Fig. 1), made in the embodiment using sensors of the first and second electric potential differences and a second electric potential difference sensor in the direction perpendicular to the profile axis, contains ground supply 2 and 3 of the first electric dipole source (current dipole) installed in the ground 1 A ₁ B ₁ ), connected to the generator 4 rectangular current pulses. To ensure synchronization of the moments of turning on and off the current pulses, the generator 4 is connected to the radio transmitter 5 with the antenna 6. The device also contains a second current dipole A ₂ B ₂ - ground 7 and 8, connected to the second generator 9 of rectangular current pulses, which are synchronized with the receiver through transmitter 10 with antenna 11.

, равной разности двух первых разностей электрических потенциалов

и

Датчик второй ортогональной разности потенциалов, состоящий из трех электродов 15-М_у1, 13-N и 16-M_y2, служит для измерения второй ортогональной разности электрических потенциалов

, равной разности двух первых ортогональных разностей электрических потенциалов

и

. Согласующий усилитель 17 предназначен для измерения первой осевой разности потенциалов

. Согласующий усилитель 18 - для измерения второй осевой разности потенциалов

. Согласующий усилитель 19 - для измерения второй ортогональной разности потенциалов

, равной разности двух первых ортогональных разностей электрических потенциалов

и

.The receiving dipole (grounding 12-M ₁ and 14-M ₂ ) of the sensor of the first axial difference is mounted on the axis of the profile in the middle between the supply dipoles. The sensor of the second axial electric potential difference, consisting of three electrodes 12-M ₁ , 13-N and 14-M ₂ , is used to measure the second axial electric potential difference

equal to the difference of the first two differences of electric potentials

and

The sensor of the second orthogonal potential difference, consisting of three electrodes 15-M _y1 , 13-N and 16-M _y2 , is used to measure the second orthogonal potential difference

equal to the difference of the first two orthogonal differences of electric potentials

and

. Matching amplifier 17 is designed to measure the first axial potential difference

. Matching amplifier 18 - for measuring the second axial potential difference

. Matching amplifier 19 - for measuring the second orthogonal potential difference

equal to the difference of the first two orthogonal differences of electric potentials

and

.

The inputs of analog-to-digital converters (ADCs) 20, 21, and 22 are connected to matching amplifiers 17, 18, and 19, and the outputs are connected to the inputs of digital filters 23, 24, and 25; the outputs of the digital filters 23, 24 and 25 are connected to a computer processing and recording unit 26, to which a radio receiver 27 is also connected, which through a receiving antenna 28 receives synchronizing pulses from generators 4 and 9.

Consider the theoretical foundations of the proposed method for its implementation and the new possibilities of geoelectro-exploration regarding the propagation of the electromagnetic field based on the damped wave equation of mathematical physics.

It is known that an electromagnetic field in a poorly conducting physical medium propagates in time t according to the differential decaying wave equation of mathematical physics for the electric field strength resulting from the first and second Maxwell equations, including in the case of its pulse change:

- оператор Лапласа;Where

- Laplace operator;

E - electric field strength, volts / m;

μ - magnetic permeability - a constant value for non-magnetic media, which include sedimentary geological rocks, and is equal to 4π · 10 ^-7 Henry / m;

σ ₀ - electrical conductivity of non-polarizable medium, Siemens;

ε is the dielectric constant, Farada / m.

(V. A. Govorkov. Electric and magnetic fields. M., Gosenergoizdat, 1960, p. 257-263) [4].

In the case of a highly conductive medium, to which sedimentary rocks belong, due to the fact that σ _{0 is} numerically many times greater than ε, the second term on the right-hand side of equation (2) is small compared to the first and is discarded (L.L. Vanyan. Fundamentals of electromagnetic sounding. M., "Nedra", 1965, p.28-30) [5]. Physically, this means that bias currents in conductive media are neglected due to their smallness compared to conduction currents. Then equation (2) takes the form

In geoelectrical exploration, this equation has a solution only for one-dimensional axisymmetric media, in particular for media with subhorizontal unboundedly extending interfaces.

At the same time, we note that in reality the geological environment is always three-dimensionally heterogeneous, since, firstly, it contains near-surface local inhomogeneities, and secondly, in general, the geological environment constantly changes its electrophysical parameters along the research profile. However, equation (3) has so far been solved only for one-dimensional axisymmetric media, including a medium of a one-dimensional horizontally layered medium with unlimited interfaces. Therefore, the use of the solution of equation (3) in inverse problems of geoelectrical exploration for the search and contouring of oil and gas deposits is permissible only in the case when in the field measurements the electric current of the source of the electromagnetic field is focused, since in this case when the difference of electric potentials under the point N is equal to zero ( 3a) the form of the field propagation of the two sources of B ₁ a ₁ a ₂ and B ₂ is almost always the same in both three-dimensional inhomogeneous medium, and in the one-dimensional - with plane subgoriz ntalnymi boundaries.

In the one-dimensional horizontal medium according to figa, on which, in particular, the straight poles A ₁ and A _{2 of} both current dipoles B ₁ A ₁ and A ₂ B ₂ are located closer to the point N equidistant from them, with equal currents in them (Fig .3b)

- разность потенциалов в точке зондирования N от действия тока

диполя B₁A₁ при выключенном диполе А₂В₂ (величина согласно фиг.3в в этой точке всегда отрицательная);Where

- the potential difference at the sensing point N from the action of the current

dipole B ₁ A ₁ with the dipole A ₂ B _{2 off} (the value according to FIG. 3c is always negative at this point);

- разность потенциалов в точке зондирования N от действия тока

диполя А₂В₂ при выключенном диполе B₁A₁ (величина в этой точке всегда положительная).

- the potential difference at the sensing point N from the action of the current

dipole A ₂ V ₂ when the dipole B ₁ A _{1 is off} (the value at this point is always positive).

It follows from formula (4) that, according to Ohm's law, the total axial component of the current density j _x under the indicated point N, the total of the alternating element-by-element switching of both current dipoles B ₁ A ₁ and A ₂ B _2, is zero according to the superposition principle.

Thus, under the sensing point, the current is focused, leading to the exclusion of the component of the current density j _{x there} .

и

в обоих токовых диполей и равенстве их расстояний до точки N условие (4) не выполняется.However, in reality, the geological environment is always three-dimensionally heterogeneous, and even with equal currents

and

in both current dipoles and the equality of their distances to point N, condition (4) is not satisfied.

и

по своим модулям отличаются в к раз, то есть для первого токового диполя B₁A₁ первая и вторая осевые разности потенциалов будут соответственно равны

и

а для второго

и

причем при расположении токовых диполей согласно фиг.3а обе вторые осевые разности потенциалов положительны.Namely, in three-dimensionally inhomogeneous media

and

in their modules they differ by a factor of time, that is, for the first current dipole B ₁ A _{1, the} first and second axial potential differences will be respectively equal

and

and for the second

and

moreover, when the current dipoles are arranged according to Fig. 3a, both second axial potential differences are positive.

To fulfill the condition of focusing the current in a three-dimensionally inhomogeneous medium in order to exclude the axial component of the current density j _x under the measuring point, expression (4) should take the form

This form is valid for geometrically located current dipoles B ₁ A ₁ and A ₂ B ₂ according to Fig.3.

To ensure the exclusion of the axial component of the density j _x under point N in the proposed method, the corresponding formulas of the measured electrical parameters are constructed, for example

where k (t _i ) is the coefficient obtained from the equation ΔU _x (t _i ) ₁ + k (t _i ) · ΔU _x (t _i ) ₂ = 0, which follows from the condition that the resulting axial potential difference of the electric field along the profile axis be equal to zero within the measuring ground area of the sounding installation.

и

этих диполей в любой трехмерно-неоднородной среде в каждой точке пространства в направлении вертикальной координаты z под точкой N в плоскости, перпендикулярной к оси профиля на всем протяжении времени переходных процессов t_i, обеспечивает равенство нулю зависящей от времени t осевой составляющей плотности тока j_x(t). Это происходит всегда независимо от того, меняется множитель К в процессе времени переходных процессов t или нет.Formula (6) regardless of the location of the current dipoles on the profile and the magnitude of the currents

and

of these dipoles in any three-dimensionally inhomogeneous medium at each point in space in the direction of the vertical coordinate z under the point N in the plane perpendicular to the axis of the profile for the entire duration of the transition processes t _i , ensures that the time-dependent axial component of the current density j _x t). This always happens regardless of whether the factor K changes during the transient time t or not.

Due to this, when solving the inverse problem, the shoulder effect is excluded, i.e. the electric field in a three-dimensionally inhomogeneous medium under the point N, described, in particular, by formula (6), always practically coincides with the field in a one-dimensional horizontally layered medium with unlimited interface.

This makes it possible to relatively stably solve the inverse problem at the sounding point N for a three-dimensionally inhomogeneous medium using the well-known analytical solution for a one-dimensional medium with horizontally layered interfaces.

There may be other ways to equalize the potentials of extreme measuring groundings: creating current grounding groups, measuring grounding groups, etc. The measuring grounding groups can be modified, for example, instead of three, four. Bipolar sources can be introduced in order to change the penetration depth of the vertical current j _z (t) and determine the vertical variability of the rocks. You can change the size of the installation. However, regardless of the installation modification, the basis of the proposed method is the equality to zero of the resulting first potential difference of the electric field based on its measurement, which eliminates the influence of the axial component of the current density j _x (t).

We also note that equation (3) is an equation of time propagation of an electromagnetic field in a non-polarizable conducting medium, which coincides with the heat conduction or diffusion equation known in mathematical physics and which is usually used in geophysics in resistance methods to study the propagation of an alternating electromagnetic field deep into the thickness of the studied geological rocks, while it is believed that the electrical conductivity σ ₀ of a particular geological horizon is the main and almost unique which determines its electrical properties, has its constant value for each horizon and does not depend on the frequency of excitation of the electromagnetic field. However, geological sedimentary rocks, when excited by the alternating low-frequency electric current used in geophysics, are characterized by the polarization η caused by them. The induced polarization is a dimensionless quantity that depends on the electrochemical activity of sedimentary rocks. It is defined as the ratio of potential differences measured on a sample of the studied rock after turning off current pulses after 0.5 seconds (ΔU _vp ) and before switching off (ΔU). This ratio is usually expressed as a percentage.

The induced polarization of sedimentary geological rocks has unique stability among physical parameters and practically does not depend on the composition of the rocks and their temperature. For ion-conducting (sedimentary) rocks, it depends on many factors: moisture and porosity, composition and concentration of the solution in the rock pores, pore structure and size, clay mineral content, etc. (V.A. Komarov. Electrical exploration by the polarization method. L., Nauka, 1980, p. 392) [6]. And, most importantly, as shown by extensive practical geoelectric studies of the proposed method at geological objects, the induced polarization carries basic information about the presence in the geological environment of a high degree of this polarization of oil and gas deposits.

It has been established (WHPelton, SHWard, PGHallof, WRSill and PHNelson. Mineral discrimination and removal of inductive coupling with multifrequency JP, Geophysies 43, 1978, p. 588-603) [7] that the electrical conductivity of sedimentary rocks is not constant , and depends on the induced polarization and on the frequency of excitation of the electric field according to the proposed, in particular, KSCole and RHCole in the form of its harmonious temporal change in the empirical formula

in which this electrical conductivity depends on ω, σ ₀ , η and τ,

where η is the induced polarization of the rocks, a dimensionless quantity, usually expressed as a percentage;

τ is the time constant determining the decay rate of the potential difference associated with the induced polarization, sec;

ω is the harmonic frequency of electrical excitation, Hertz;

c is a dimensionless exponent, which, although it is not a physical parameter of rocks, σ (iωσ ₀ ητ) also depends on it.

The induced polarization η at low frequencies of electric excitation, unlike the dielectric constant ε, is numerically not so small compared to the electrical conductivity σ ₀ for sedimentary geological rocks, measured, for example, at high frequency currents (ω → ∞), when, as can be seen from formula (8), the induced polarization does not occur. Therefore, the polarization caused by studying with the aim of searching and delineating the oil and gas deposits of the geoelectric parameters of sedimentary geological rocks at low-frequency alternating current cannot be neglected. It is known (Electrical Exploration. Handbook of Geophysics. Ed. V.K. Khmelevsky and others M., Nedra, 1989, Book Two, p. 99-102) [8] that for certain sedimentary geological rocks in 0.5 sec after switching off the exciting current pulse, the magnitude of the potential difference caused by polarization, despite its intense decline, still retains levels whose numerical values are from 0.2% to 10% of the numerical values of the potential differences of the direct field associated with the electrical conductivity σ ₀ , measured as noted above at high frequency currents when called Single polarization is not observed. To keep formula (8) in shape, we write the thermal equation (3) for the case of a harmonic change in the magnitude of the electromagnetic field over time, bearing in mind that

and given that

and

Then equation (3) for a conducting non-polarizable medium, taking into account transformation (9), takes the form

But since the electrical conductivity of sedimentary rocks is unstable, and depends on the induced polarization and on the excitation frequency according to formula (8), equation (11), taking this formula into account, acquires four defining properties of the polarized medium of parameter σ ₀ , η, τ and c instead of one σ ₀ and for the case of a harmonic change in the magnitude of the electromagnetic field with time takes the form

and in general terms, taking into account (8),

The replacement of the frequency-independent conductivity σ ₀ , which is present in equation (3), with the frequency-dependent σ (iω) present in equation (13), is mathematically correct and theoretically proved (A.K. Kulikov, S. A. Shemyakin. phase method of induced polarization. Moscow "Nedra" 1978, pp. 24-26) [2].

Equation (13) becomes essentially close to the decaying wave equation (2) for the electric field at low frequencies, according to the laws of which an alternating electromagnetic field penetrates the Earth not only due to diffusion induction currents caused by the electrical conductivity σ ₀ , but also due to currents “Displacements” caused by the polarization η of the same rocks. The latter circumstance suggests that the possibilities of geoelectrical exploration for prospecting and contouring oil and gas deposits on a low-frequency alternating (harmonic or pulsed) current are higher than previously thought. These possibilities are realized (at least) under two conditions: the first - when the range of measured electrical normalized parameters expands to three necessary for the correct solution of equation (12), and the second - when the electric current is focused in order to eliminate the axial component of the current density j _x ( t).

Realization of new opportunities for geoelectrical exploration is achieved by the proposed method. And the fact that equation (12) is essentially close to the decaying wave equation for the electric field, equation (2), it is easy to verify by expanding formula (8) in the Taylor series with respect to the frequency difference ω-ω ₀ (where ω ₀ is the frequency following pulses of the excitation current), using, in particular, only two members of this series due to its rapid convergence at ω ₀ <τ ^-1 (which is usually done in practice). With this assumption, we obtain the equation

, но все же не настолько как ε по сравнению с σ₀ в проводящей неполяризующейся среде, и пренебрегать вторым членом этого уравнения уже не допустимо.As can be seen, equation (14) in form does not differ from the decaying wave equation for the electric field strength (2) for the case of a pulsed change in the magnitude of the electromagnetic field. And although the coefficient at -ω ² · E (iω) is less than the coefficient at

, but still not so much as ε in comparison with σ ₀ in a conducting non-polarizable medium, and it is no longer permissible to neglect the second term of this equation.

Equation (12) is considered to be inherently close to equation (2), and not equal to it analytically because in its derivation the empirical formula (8) was used due to the lack of an analytical formula for the relationship between the electrical conductivity σ (iωσ ₀ ητ) and polarization induced η.

For the proposed method, the problem of detecting oil and gas deposits in the studied rock mass as a mathematical inverse problem is solved according to equation (13) as a function of time, i.e. in a function depending on the time of penetration depth of the electromagnetic field, in three medium parameters independent from each other: electrical conductivity σ ₀ ; caused by polarization η; the time constant τ of the decay of the difference in electric potentials caused by polarization; and according to the fourth, non-environmental parameter, exponent c, which follows from the empirical formula (8).

This problem, as an inverse mathematical problem, is solved for the proposed first variant of the method with sensors of the first and second axial differences of electric potentials and with a sensor of the second difference of electric potentials in the direction perpendicular to the axis of the profile by using the entire array determined in this way, at least three sources of normalized electrical parameters independent of current strength:

in current pauses at time t _i (0≤i≤n) equal to t ₀ , t ₀ + Δt, t ₀ + 2Δt, t ₀ + 3Δt, etc. to t ₀ + nΔt, i.e. to the end of the pause, and the differential equation of mathematical physics (12) for the electric field strength of a dipole source in an electrochemically polarized conducting medium, in particular, for example, one of the methods for solving the inverse mathematical problem is the selection method (A.N. Tikhonov, V.Ya. Arsenin, Methods for Solving Ill-posed Problems, Moscow, Nauka 1979. p. 37-43) [9]. At the same time, to reduce the number of selection options, the available data on the model of the studied geological environment are used, for example, drilling of reference or parametric wells, which are usually drilled everywhere with a rare step, or seismic data, if the latter has already been carried out in the study area. In the absence of any a priori data on the geological section, which, as a rule, is most often encountered in prospecting studies, the inverse problem is also solved, but with an increased number of selection options.

In the end result, by solving the inverse problem, we obtain a model of the medium that is closest to the real one in terms of geometric structure and in the values of the parameters σ ₀ , η and τ for each of its elements and, as a consequence of this, separate these three parameters. And finally, three time sections σ ₀ , η, and τ are built: along the vertical coordinate as a function of the time of the transition process in a pause of the current functionally related to the depth of penetration of the field, and therefore to the depth of each horizon found as a result of the solution inverse problem of the model of the environment; along the horizontal coordinate - as a function of the distance between the sensing points on the Earth's surface according to a given profile; and the values of the electrophysical parameters σ ₀ , η and τ included in equation (12) are represented by the digital scale attached to each section in a color image in a color gamut.

Similarly, the inverse mathematical problem is solved for the second variant of the method with axial sensors of the first and second electric potential differences, where the entire array of three sources of normalized electrical parameters independent of the current strength is also used:

It should be noted that the measured second electric potential difference by the orthogonal sensor, the axis of which is perpendicular to the axis of the sounding profile, is free from the electric conductivity of the upper layer of the geoelectric section and is therefore much less affected by electrodynamic effects than the measured differences by axial sensors (Fig. 4). Therefore, when mapping low-contrast oil and gas deposits that are low in contrast due to polarization, the method using the second difference orthogonal sensors is most effective. And especially in those cases when the geological deposits in which the deposit is located are covered by a layer with high electrical conductivity.

Investigations by the proposed method in oil and gas fields established that in the presence of an oil or gas reservoir, regardless of the type of trap and its geometrical shape, all three parameters (electrical conductivity σ ₀ , induced polarization η and time constant τ) within the reservoir contour take the form of an anomaly in the depth of the section, where this deposit is located.

Concrete example

Figure 1 presents the block diagram of the equipment for implementing the proposed method. The block diagram shows current dipoles A ₁ B ₁ (2 and 3) and A ₂ B ₂ (7 and 8) grounded in the ground 1, fed by generators 4 and 9 of rectangular current pulses with pauses between them. On the axis of the dipoles at a predetermined distance from them, using the measuring earths, in the current pause, at a given time interval Δt, the set of differences ΔU _x (t _x ), Δ ² U _x (t _x ) and Δ ² U _y (t _x ) is measured throughout the existence of pauses. All of the indicated measured differences are amplified by amplifiers 17, 18, and 19. To ensure the measurement accuracy necessary to identify the features of the transition curves of field formation in current pauses associated with polarization of the studied rocks, the differences measured by amplifiers 17, 18, and 19 are digitized by analog digital converters (ADC) 19, 21 and 22 with a resolution of 24 or more. To implement the proposed method, a measuring device with a twenty-four-digit ADC has been developed and manufactured. In this device, after twenty-four digitization of the measured signals, the latter are filtered out from random interference using multi-link digital filters 23, 24 and 25. Filtered useful signals from the outputs of digital filters 23, 24 and 25 are fed to the input of a computer processing and recording unit 26.

To ensure synchronization of the moments of turning on and off the current pulses with the moments of measurement in the receiver of the receiving signals, radio transmitters 5 and 10 and a radio receiver 27, respectively, with transmitting antennas 6 and 11 and receiving 28 are used.

To determine the necessary three normalized electrical parameters (15) and (16), a series of instantaneous values of the first and second differences of the electric potentials of transients ΔU _x (t _i ), Δ ² U _x (t _i ) and Δ ² U _y (t _i ) is measured in pauses for the entire duration of the existence of pauses between current pulses. A series of difference values is also determined from each two adjacent instantaneous values of the first and second potential differences along the entire duration of the existence of pauses between current pulses. Plots of one of the current pulses and the measured i-th instantaneous values of the first and second potential differences in one of the pauses are shown in Fig.3. Indices 1 and 2 in formulas (15) and (16) denote that the measurement of electrical parameters was carried out with separate excitation of the first and second current dipoles.

Figure 4 shows the results of mathematical modeling by the proposed method for a five-layer model of a medium with subhorizontal, infinitely extended interfaces. See the data of this model in the table of mathematical modeling in a layered medium. In the lower left square of the table, the parameters of the layers of the original model are given (h - kilometers of each layer, ρ - Ohm · m and η - induced polarization - percent). In the lower middle square, the change in the resistivity of the second layer to 500 Ohm · m relative to 100 Ohm · m of this layer in the original model is given. The lower right square shows the change in the induced polarization of the second layer to 10% relative to 0.5% of this layer in the original model.

In the first column of the graphs (figure 4) the results of modeling by parameters

For the original model (solid curves) and for the model with anomalous electrical resistivity of up to 500 Ohm · m in the second layer (dashed curves).

The second column of the graphs gives the results of modeling by parameters

For the original model (solid curves) and for the model with anomalous induced polarization of up to 10% in the second layer (dashed curves).

On all eight graphs, the abscissa gives time in seconds on a logarithmic scale. The length of the sounding installation is 1.6 km.

The proposed method is implemented as a complex of feeding, measuring and processing equipment. As noted above, studies of the proposed method in oil and gas fields established that in the presence of an oil or gas reservoir, regardless of the type of trap and its geometrical shape, all three parameters σ ₀ , η and τ within the reservoir contour take the form of an anomaly in the depth of the section where this deposit is located, and the coefficient of success of the geophysical search for oil and gas deposits using the proposed method is significantly increased. The latter gives a significant economic effect in the search and exploration of hydrocarbon accumulations.

The table of mathematical modeling in a layered environment Layer number source model resistance change (layer 2) polarization change (layer 2) h, km ρ, Ohm η,% h, km ρ, Ohm η,% h, km ρ, Ohm η,% one. one twenty one one twenty one one twenty one 2. one one hundred 0.5 one 500 0.5 one one hundred 10 3. 2 fifty 0.1 2 fifty 0.1 2 fifty 0.1 four. 0.5 twenty 0.05 0.5 twenty 0.05 0.5 twenty 0.05 5. ∞ 1000 0.0 ∞ 1000 0.0 ∞ 1000 0.0

Claims (2)

1. The method of geoelectrical exploration, in which an electromagnetic field is excited along the axis of the sounding profile in the thickness of the medium under investigation, passing through it a periodic sequence of rectangular current pulses with pauses after each of them alternately from two dipole electric sources, in each pause between current pulses throughout the entire time the existence of this pause at discrete time points with a constant time interval measure the sequence of instantaneous values of the first and second axial differences of potentials with the help of measuring groundings located between dipole electric sources, simultaneously at the same discrete time points in each pause between current pulses throughout the entire lifetime of this pause measure the sequence of instantaneous values of the second differences of electric potentials in the direction perpendicular to the profile axis, this provides focusing of the current to eliminate the axial component of the current under the sensing point, maintaining the equality to zero result ruyuschey potential difference between the outer measuring earths, calculated from three independent sets of current dipole sources normalized electrical parameters of the measured electrical potential difference values

Where k (t _i ) is the coefficient obtained from the equation ΔU _x (t _i ) ₁ + k (t _i ) · ΔU _x (t _i ) ₂ = 0; Δt is the time interval between the two nearest measured instantaneous values of the first and second differences of electric potentials throughout the existence of a pause; ΔU _x (t _i ) ₁ , ΔU _x (t _i ) ₂ Δ ² U _x (t _i ) ₁ , Δ ² U _x (t _i ) ₂ - instantaneous values of the first and second axial differences of electric potentials, measured in pauses of current on throughout the existence of each of these pauses from its beginning to the end at given equal time intervals Δt, when currents are supplied, respectively, to the first and second dipole electric sources; Δ ² U _y (t _i ) ₁ , Δ ² U _y (t _i ) ₂ - instantaneous values of the second axial differences of electric potentials, measured in the direction perpendicular to the axis of the profile, in the pauses of current throughout the existence of each of these pauses from it beginning to the end at equal time intervals Δt when applying currents, respectively, to the first and second dipole electric sources; Δ ² U _x (t _i , Δt) ₁ , Δ ² U _x (t _i , Δt) are the differences between the separated time intervals M by the two nearest instantaneous values of the second axial differences of electric potentials, measured in pauses of current throughout the existence of each of these pauses; using the values of normalized parameters and the differential equation of mathematical physics for the electric field strength of a dipole source in an electrochemically polarized conducting medium

Where

- Laplace operator;

- the electric field strength of the dipole source, expressed in the equation for the case of a harmonic change in the magnitude of the electric field over time; σ (iωσ ₀ ητ) is the frequency-dependent conductivity of the elements of the medium; σ ₀ is the electrical conductivity of the elements of the medium without taking into account the effect of induced polarization; η is the coefficient of their induced polarization; τ is the decay time constant of the potential difference caused by polarization, they solve the mathematical inverse problem, determine three electrophysical parameters inherent in each element of the medium: electrical conductivity σ ₀ , induced polarization η, and decay time constant of the potential difference caused by polarization, and construct three time sections from these parameters. 2. A method of geoelectrical exploration, in which an electromagnetic field is excited along the axis of the sounding profile in the thickness of the medium under investigation, passing through it a periodic sequence of rectangular current pulses with pauses after each of them alternately from two dipole electric sources, in each pause between current pulses throughout the entire time the existence of this pause at discrete time points with a constant time interval measure the sequence of instantaneous values of the first and second axial differences ble potentials, while providing focusing current component to exclude the axial current under the sensing point while maintaining the vanishing of the resultant potential difference between the outer measuring earths; from the values of the measured electric potential differences, three sets of dipole sources of normalized electrical parameters independent of the current strength are calculated

Where k (t _i ) is the coefficient obtained from the equation ΔU _x (t _i ) ₁ + k (t _i ) · ΔU _x (t _i ) ₂ = 0; Δt is the time interval between the two nearest measured instantaneous values of the first and second differences of electric potentials throughout the existence of a pause; ΔU _x (t _i ) ₁ , ΔU _x (t _i ) ₂ Δ ² U _x (t _i ) ₁ , Δ ² U _x (t _i ) ₂ - instantaneous values of the first and second axial differences of electric potentials, measured in pauses of current on throughout the existence of each of these pauses from its beginning to the end at predetermined equal time intervals Δt, when currents are supplied, respectively, to the first and second dipole electric sources; ΔU _x (t _i , Δt), ΔU _x (t _i , Δt) ₂ , Δ ² U _x (t _i , Δt) ₁ , Δ ² U _x (t _i , Δt) ₂ - the difference between the separated time interval Δt the two closest instantaneous values of the first and second axial differences of electric potentials, measured in pauses of current throughout the existence of each of these pauses; using the values of normalized parameters and the differential equation of mathematical physics for the electric field strength of a dipole source in an electrochemically polarized conducting medium

Where

- Laplace operator;

- the electric field strength of the dipole source, expressed in the equation for the case of a harmonic change in the magnitude of the electric field over time; σ (iωσ ₀ ητ) is the frequency-dependent conductivity of the elements of the medium; σ ₀ is the electrical conductivity of the elements of the medium without taking into account the effect of induced polarization; η is the coefficient of their induced polarization; τ is the decay time constant of the potential difference caused by polarization, they solve the mathematical inverse problem, determine three electrophysical parameters inherent in each element of the medium: electrical conductivity σ ₀ , induced polarization η, and decay time constant of the potential difference caused by polarization, and construct three time sections from these parameters.

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