RU2107313C1 - Method of geophysical studies of holes of complex configuration based on usage of directed wide-band electromagnetic pulses excited by cylindrical slot array - Google Patents

Abstract

FIELD: geophysics. SUBSTANCE: proposed method is meant for determination of electric and geometric parameters of zones close to holes in holes of complex configuration. In accordance with method probe in the form of cylindrical slot array is excited by wide-band electromagnetic pulses with duration in the order of 10^-9 s. Component of magnetic field is measured by receiving antenna and measurement results are compared with results of mathematical modeling. Electric and geometric parameters of inhomogeneities of space close to hole are determined on basis of minimization of vector of closure error. EFFECT: enhanced authenticity of method. 2 dwg

Description

 The invention relates to geophysics and is intended for research in wells when studying a geological section, identifying minerals, monitoring the technical condition of wells and developing fields.

 A method is proposed for geophysical studies of oil and gas wells of complex configuration (vertical, inclined and horizontally directed) to determine the electrical parameters (dielectric constant and electrical conductivity) and the interfaces of layered inhomogeneous media in the near-wellbore zones.

The method is based on the registration and mathematical processing of broadband electromagnetic pulses with a duration not exceeding 10 ^-9 s, excited and received by a cylindrical antenna array.

 The invention is illustrated by the results of mathematical modeling of the propagation of electromagnetic pulses in heterogeneous near-wellbore spaces.

где η_o= 120π = 376,99 , ε_r - относительная проницаемость среды. Из формулы (1) следует, что глубина проникновения электромагнитного поля в околоскважинное пространство с проводимостью σ = 1 См/м составляет всего δ = 0,048 м. Принимая во внимание такое незначительное проникновение электромагнитной волны высокой частоты, автор патента R. Freedman указывает ограниченную область применения своего изобретения, состоящую в микродиэлектрическом сканировании околоскважинных зон с целью определения структурной анизотропии и трещиноватости вблизи стенки скважины.The closest analogue is the microdielectric scanning method for near-wellbore zones, proposed by: R. Freedman, Method and apparaus for measuring azimuthal as well as longitudinal waves in formation traversed by a borehole, United States Patent Number: 5,168,234; Date of Patent: Dec. 1, 1992. In the cited patent R. Freedman proposed a method for studying near-wellbore areas using cylindrical antenna arrays that excite a high-frequency electromagnetic field with a fixed frequency of 1.1 • 10 ⁹ Hz. In this case, longitudinal and azimuthal waves are alternately excited and measured. A fundamental limitation of the method proposed by R. Freedman is the relatively small depth of penetration of a high-frequency electromagnetic field (equal to δ = 0.03 - 0.1 m) in the near-wellbore space for wells drilled using flushing fluids with electrical resistivity σ ≥ 0.1 , S / m (note that the vast majority of oil and gas wells in Russia and abroad are drilled using flushing fluid with σ> 0.1 S / m). An estimate of the penetration depth δ for high frequencies of the order of 10 ⁹ Hz can be performed according to the formula

where η _o = 120π = 376.99, ε _r is the relative permeability of the medium. From formula (1) it follows that the depth of penetration of an electromagnetic field into a near-wellbore space with a conductivity of σ = 1 S / m is only δ = 0.048 m. Considering such a small penetration of an electromagnetic wave of high frequency, the author of R. Freedman indicates a limited scope of his invention, consisting in microdielectric scanning of the near-wellbore zones in order to determine the structural anisotropy and fracture near the borehole wall.

The proposed method for geophysical research of wells, based on the use of broadband electromagnetic pulses, in contrast to the method presented in the patent of R. Freedman, has two fundamentally important advantages that provide: a) the depth of investigation of the inhomogeneous space of the order of 1-3 m with a resolution of ΔL ≤ 0.03 m;
b) quantitative determination of the electrical and geometric parameters of the near-wellbore space in the azimuthal and longitudinal direction of the wells.

A method of geophysical studies of wells of complex configuration for determining the electrical and geometric parameters of near-wellbore zones using a cylindrical antenna array, which is excited by broadband electromagnetic pulses of about 10 ^-9 s in duration, measures the magnetic field component with a receiving antenna, compares the measurement results with the results of mathematical modeling and based on minimization of the residual vector determines the electrical and geometric parameters of the inhomogeneity awns borehole environment.

 Known cylindrical probes with electromagnetic excitation at a fixed frequency do not have high penetration in rocks and other inhomogeneous dielectric media that are being studied.

The claimed invention proposes a method for researching rocks with probes with a cylindrical antenna array that excites ultrashort spatially directed broadband electromagnetic pulses. The method is based on the selection of informative signals on the receiving antenna devices of the probe: direct signal; side waves and waves, one- and many-reflected from the interfaces of inhomogeneities, with the moments of their arrival and the subsequent analysis of the amplitude and phase of each incoming signal. Receiving antenna devices are located on the cylindrical surface of the probe at different distances y _m from the transmitting antenna. Processing the results of measuring the response of the electromagnetic field is based on the application of a mathematical model of the antenna array in the well, surrounded by a layered-inhomogeneous space. As a result of comparing the measured response of the electromagnetic field to the pulse excited by the antenna array, with the corresponding data of mathematical modeling and minimizing the residual vector, the electrical and geometric parameters of the inhomogeneous near-wellbore space are determined.

The use of short video pulses with a duration of the order of 10 ^-10 - 10 ^-9 s is a very effective method of radar detection and recognition of natural and artificial subsurface formations. The broadband of such short pulses provides a penetration depth of the order of 1–3 m in media with large losses with a conductivity σ exceeding 1 S / m and a high resolution when studying an inhomogeneous medium.

.The low-frequency part of the broadband electromagnetic pulse has a large penetration depth

.

According to this formula, for the components of the spectrum of the pulse with a frequency f = 10 ⁵ Hz, the penetration depth is δ = 1.59 m. A comparison of the penetration depth of the high-frequency electromagnetic field (formula 1) and the low-frequency field (formula 2) shows a significantly greater efficiency in the use of broadband signals with pulse duration 10 ^-10 - 10 ^-9 s.

 In addition, the high-frequency part of the spectrum of the transmitting antenna serves to exacerbate the emitted pulse, which is necessary so that its amplitude decreases to the required low level at the time of arrival of a weak reflected pulse to the receiving antenna. The shape of the pulse and its duration determine the resolution of the proposed method.

The resolution is characterized by the minimum possible thickness of the heterogeneity layer, the determination of which is provided by this electromagnetic pulse method of sounding. With a pulse duration of 10 ^-9 s, the resolution ΔL will be of the order of 0.03 m. With a decrease in the pulse duration, the resolution of the method increases, i.e. ΔL <0.03 m.

 To disclose the essence of the proposed method, consider a mathematical model that reflects the principles of the proposed method for logging wells of complex configuration.

- дельта-функция Дирака, f(t) - заданная функция времени, m₀ - амплитуда дипольного момента. Функция f(t) описывает следующие нестационарные процессы возбуждения электромагнитного поля: включение монохроматического диполя в момент времени t = 0; прямоугольный импульс произвольной длительности τ , гауссов импульс вида f(t) = exp[β²(t-τ_o)²] и др. При этом переменный магнитный момент тока I(t) диполя равен dm/dt = I(t).The study of unsteady processes of propagation of electromagnetic pulses is based on the consideration of a three-layer medium with media interfaces representing infinite parallel planes. Suppose a slot antenna array is used. According to the electrodynamic principle of equivalence, the radiation from a gap cut in an ideally conducting surface can be replaced by the action of a horizontal magnetic dipole with a current moment I. A Cartesian coordinate system with the xy plane (i.e., the z = 0 plane, where the z axis is perpendicular to the interfaces of the media) is introduced ), which is ideally conductive and simulates the lateral surface of the probe. An unsteady magnetic dipole is located on a perfectly conducting probe surface at the origin of the coordinate system with a moment

is the Dirac delta function, f (t) is the given function of time, m ₀ is the amplitude of the dipole moment. The function f (t) describes the following non-stationary processes of excitation of the electromagnetic field: the inclusion of a monochromatic dipole at time t = 0; a rectangular pulse of arbitrary duration τ, a Gaussian pulse of the form f (t) = exp [β ² (t-τ _o ) ² ], etc. In this case, the alternating magnetic moment of the current I (t) of the dipole is dm / dt = I (t).

,
где
G(R, p) = exp(ik₁(p)R)/R - функция Грина,

, M = (x,y,z),

, p - комплексная переменная преобразования Лапласа, J_0,1(z) - функции Бесселя, J_x(p) = pm(p) - преобразование Лапласа момента магнитного тока J_x(t) = dm_x(t)/dt,

, Reγ₁> 0 ,

, Imk₁>0, ε₁(p) = ε₀ε_r1+σ₁/p , ε_r1 и σ₁ являются относительной диэлектрической проводимостью и проницаемостью 1-го слоя; всюду μ₁= μ_0/ . Неизвестные функции g_x, g_z определяются из условий непрерывности тангенциальных компонент электрического и магнитного полей на границах разделов сред.The Laplace transform of the Maxwell equations with respect to time variable gives an image of the components of the vector potential A $\genfrac{}{}{0ex}{}{\text{(1)}}{\text{x}}$ (M, p) and A $\genfrac{}{}{0ex}{}{\text{(1)}}{\text{z}}$ (M, p) in the first layer (adjacent to the xy plane):

,
Where
G (R, p) = exp (ik ₁ (p) R) / R is the Green function,

, M = (x, y, z),

, p is the complex variable of the Laplace transform, J _0,1 (z) are the Bessel functions, J _x (p) = pm (p) is the Laplace transform of the magnetic moment J _x (t) = dm _x (t) / dt,

, Reγ ₁ > 0,

, Imk ₁ > 0, ε ₁ (p) = ε ₀ ε _r1 + σ ₁ / p, ε _r1 and σ ₁ are the relative dielectric conductivity and permeability of the 1st layer; everywhere μ ₁ = μ _{0 /} . The unknown functions g _x , g _{z are} determined from the continuity conditions of the tangential components of the electric and magnetic fields at the interfaces.

.We are interested in the values of the x-component of the magnetic field in the receiving antennas with different coordinates M = (0, y _m , 0):

.

.Non-stationary solutions can be formally represented as the inverse Laplace transform:

.

 A set of computer programs has been created for calculating the components of the magnetic field at the observation point for various parameters of layered media of pulse types.

, m = 0,1, . .., h - толщина первого слоя. Кроме того, полное нестационарное электромагнитное поле в точке наблюдения может также включать в себя боковые волны различных индексов. Время прибытия боковой волны индекса m (m = 1,2,.. .) равно

.From the formulas it follows that the signal received at the observation point M is the sum of the direct signal, as well as a set of waves that have experienced 0, 1, 2, ... n reflections from the interfaces of the media and from the perfectly conducting plane. For example, in the case of a two-layer medium, the moments of arrival of a signal that has experienced m reflections from the interface of two media will be equal to:

, m = 0,1,. .., h is the thickness of the first layer. In addition, the total non-stationary electromagnetic field at the observation point may also include side waves of various indices. The arrival time of the lateral wave of index m (m = 1,2, ...) Is equal to

.

These waves exist when ε _r1 > ε _r2 and t $\genfrac{}{}{0ex}{}{\text{(lat)}}{\text{m}}$ <t _m . The observed times of arrival of signals of various types, their amplitudes and phases make it possible to determine the parameters of a multilayer medium.

At each of the receiving antennas located at the points M = (0, y _m , 0) (y _m is the distance from this receiving antenna to the transmitting antenna) on the probe generatrix, the response of the x-component of the magnetic field is measured. Examples of the calculation results of the x-component of the field versus time for various media are presented in FIG. 12.

, c = 3•10⁸.In FIG. Figure 1 shows the response of the field component H _x to the influence of a magnetic dipole in a two-layer medium (σ ₁ = 0.1 S / m, ε _r1 = 80, σ ₂ = 0.005 S / m, ε _r2 = 1) with a layer thickness h = 0.55 m, y _m = 1 m, time is normalized:

, c = 3 • 10 ⁸ .

.In FIG. Figure 2 shows the diffusion-wave effect of the propagation of the magnetic field response to the excitation of a magnetic dipole by a Gaussian pulse in a two-layer medium with a high conductivity of the first layer σ ₁ = 1 S / m, ε _r1 = 40, σ ₂ = 0.005 S / m, ε _r2 = 4 point M (0, y _m , 0), y _m = 0.5 m, for various values of the layer thickness h = 0.1 m; 0.2 m; 0.3 m;

.

 The use of the created set of programs that implement the mathematical model of the propagation of electromagnetic pulses, and the analysis on its basis of the observed arrival times of signals of various types, their amplitudes and phases (for which a system of nonlinear algebraic equations is composed) allow us to determine the geometric and electrical parameters of the inhomogeneous near-wellbore space.

 The method of geophysical research of wells of complex configuration consists in analyzing and comparing the results of measuring the response of the electromagnetic field to a pulse excited by an antenna array with the corresponding mathematical modeling data, followed by minimizing the residual vector to determine the electrical and geometric parameters of an inhomogeneous near-wellbore space.

Claims (1)

The method of geophysical research of wells of complex configuration by cylindrical probes with electromagnetic excitation, designed to determine the electrical and geometric parameters of the near-wellbore zones, characterized in that the probe is made in the form of a cylindrical antenna array, which is excited by broadband electromagnetic pulses of about 10 ^{- 9} s in duration, and is measured by a receiving antenna component magnetic field, compare the measurement results with the results of mathematical modeling and based inimizatsii residual vector is determined electrical and geometric parameters of inhomogeneities borehole environment.

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