Method for downhole measurement of formation parameters.

0001This invention relates to an apparatus and method for downhole measurement of formation parameters.

0002After a well has been drilled but before it has been cemented, it is important to be able to make measurements along the borehole to determine properties of the formations penetrated by the well. Useful information can be obtained by measuring formation resistivity and the dielectric constant of the materials that make up the formations. The dielectric of space serves as a reference of 1.00. The dielectric of oil is about 2.00. Various sand and rock formations provide dielectric measurements of about 4.0 to about 10.0. The dielectric of water, however, can range quite high, even as high as 80.0 for relatively pure water. Any impurities in the water may lower the dielectric somewhat, but water can nevertheless be distinguished by its high dielectric.

0003We have now devised a method and apparatus especially (but not exclusively) useful for dielectric measurements.

0004According to one aspect of the invention, there is provided apparatus for making downhole measurements of earth formations, which apparatus comprises: <ul id="ul0001" list-style="none"><li>(a) a sonde adapted to be lowered in a well borehole for engagement with the sidewall of the borehole;</li><li>(b) a transmitting antenna supported by said sonde in contact with the borehole wall for transmitting microwave electromagnetic signals of a chosen wave length into the adjacent formation;</li><li>(c) a receiving antenna mounted at a distance from said transmitting antenna and supported by said sonde in contact with the borehole wall for receiving the transmitted microwave signals;</li><li>(d) measuring means connected to said transmitting antenna and receiving antenna for making measurements related to microwave electromagnetic signals transmitted therebetween wherein said measurements are made for signals transmitted through formations between said antennae; and</li><li>(e) means for determining formation parameters from said measurements.</li></ul>

0005In another aspect, the invention provides a method of measuring formation parameters, eg. dielectric resistivity and magnetic permeability values, of a formation along a well borehole comprising the steps of: <ul id="ul0002" list-style="none"><li>(a) transmitting microwave electromagnetic signals from a transmitter antenna into a formation adjacent to a well borehole sidewall;</li><li>(b) receiving the transmitted signal at a receiving antenna means spaced from the transmitting antenna means;</li><li>(c) making measurements of amplitude and relative phase of the transmitted signal at the time of transmission and the received signal at the time of reception;</li><li>(d) determining from said measurements an equivalent two port reciprocal electrical network representative of the formation between said transmitter antenna and said receiver antenna; and</li><li>(e) from said equivalent network, determining a value of dielectric of the formation.</li></ul>

0006The apparatus and method of the invention are able to measure dielectric as a means of distinguishing the nature of a formation encountered along the well borehole. This works even in a mixed region where the formation is made of two materials, one example being a water bearing sand. This process can be used in formations of three materials also, such as oil and water in sand. The dielectric is determined by the relative percentages and respective dielectrics, making up the formation. In this instance, the value is given by the relationship: D = f₁d₁^m + f₂d₂^m where m is a complex number. In the foregoing, the fractions f₁ . . . f_n represent the respective percentages of the materials in the formation, while the respective material dielectrics are indicated by the symbol d₁ . . . d_n. For instance, if a formation is 1/2 fresh water and the remainder sand the foregoing equation by itself will not enable determination of the fractions of sand and water, but other measurements providing other data enable the fractions of sand and water to be found. The present invention is very useful in locating water-bearing formations and provides output data indicative of the presence thereof, and coupled with other data can even indicate the percentage fraction of water in a given formation. By estimation of water in a particular formation, other conclusions can be drawn regarding that and adjacent formations which aid and assist in well completion procedures.

0007The apparatus of the invention comprises a microwave transmitting system supported in a sonde having a transmitter antenna which transmits through the adjacent or near formations to a receiver antenna. Microwave frequencies are used and ideal frequencies are in the range of about 30 megahertz to 30 gigahertz or more. The system preferably includes a transmitter oscillator connected with an output amplifier providing a continuous wave (CW) signal through a coupling circuit to the transmitter antenna. In a preferred arrangement, a portion of the output signal is applied through a mixer to beat with a signal from a local oscillator to provide a reference signal to a measuring circuit. Part of the CW signal applied to the antenna is reflected back into the transmitter circuity, and the reflected signal is mixed with the local oscillator signal to produce a reflected signal for the measuring circuit. The received signal is obtained through the receiver antenna and, in a preferred arrangement, is also mixed with the signal from the local oscillator to provide a signal for the measuring circuit. The measuring circuit makes separate measurements of the incident reflected and transmitted signals. These measured signals can be converted into a suitable format by an A/D converter, and are output for further manipulation to determine values of the dielectric. The procedure is usually carried out at selected radial depths, preferably utilizing a sonde supported pad with one or more receiver antennae thereon. Measurements are made along the borehole at a variety of depths. The sonde pad is pushed to the side of the borehole so that it is brought into intimate contact with the sidewall of the well borehole, and such measurements are analyzed as will be described. This provides data regarding the dielectric of formations and is thus useful in further analysis of the producing formations.

0008In order that the invention can be more fully understood, reference is made to the accompanying drawings illustrating embodiments of the invention. Referring to the drawings: <ul id="ul0003" list-style="none"><li>FIG. 1 shows an embodiment of sonde and pad supported dielectric measuring system in accordance with the teachings of the present invention, wherein antennae for a transmitter and for one or two receivers are positioned against the sidewall of a well bore;</li><li>FIG. 2 is an example of an equivalent circuit of certain components of the system shown in Fig. 1; and</li><li>FIG. 3 is an example of a graph of measurements of various values of dielectric.</li></ul>

0009Referring to Fig. 1 of the drawings, a sonde (10) is supported on a logging cable 12. The sonde is a tool lowered into the well borehole 14 for making measurements against the sidewall and into the formations. To this end, a backup pad 16 is incorporated for deflecting the sonde to the side thereby enabling a sensor pad 15 on the sonde to contact the sidewall. Measurements are made in the formation 18 penetrated by the well borehole and also as the sonde 10 is thereafter raised on the logging cable 12.

0010The cable 12 passes over a sheave 20 and is spooled on a drum 22. The cable is supplied in substantial length to enable a very deep well to be logged. The logging cable 12 includes one or more conductors through which important data are delivered to the surface, and the data are output from the cable to a central processor unit (CPU) 24. The data are then output to a recorder 26 for archive purposes, the data being recorded as a function of depth in the well. Depth measurement is provided by a mechanical or electrical depth measuring apparatus 28 which provides the depth of the measurements exemplified at the formation 18.

0011The sensor pad 15 supports a transmitter antenna 30. It also supports a receiver antenna 32. As desired, a second receiver antenna 34 is likewise included. Two receivers can be used to provide additional benefits. However, for simplicity, only the receiver antenna 32 is shown connected to the attached circuitry. If desired, duplicate circuitry can be connected with the receiver antenna 34 so that an additional measurement can be obtained.

0012The antenna 30 transmits a high frequency microwave CW signal outwardly into the formation 18 so that characteristics of that formation can be measured. Characteristics measured in that formation include formation dielectric in accordance with the teachings of the present disclosure. The radiation is scattered with a portion of the signal being received at the receiver antenna 32. The transmission path through the formation 18 encodes formation information into the received signal as described.

0013The remainder of the system shown in Fig. 1 comprises a transmitter oscillator 42 to form the CW signal to be transmitted. The CW signal is provided to an output amplifier 44 and is amplified to a suitable amplitude. It is output through a coupling circuit 46 to provide the output signal to the transmitter antenna 30. A local oscillator 48 forms a frequency useful in beating with the transmitted frequency in a mixer circuit 50. The mixed output is then delivered to a measuring circuit 52 which makes the necessary measurements, including amplitude and phase shift. A portion of the transmitter signal is reflected at the antenna 30 and that portion is returned to a mixer circuit 60 for mixing with the local oscillator signal. The mixed signals are applied to the measuring circuit for amplitude and phase measurement. In addition, the receiver antenna 32 is connected with a mixer circuit 54, and the beat difference is then delivered to the measuring circuit 52. The measuring circuit 52 again provides output signals reflecting amplitude and phase shift measurements to the A/D converter 56 which forms suitable output information in a proper format to a telemetry circuit 58. The output data are transferred by telemetry to the logging cable 12 which includes one or more conductor paths. Timing of all this apparatus is easily controlled because the transmitted and received signals are CW signals and hence are free of timing restraints. The measuring circuit 52 is switched to make all three measurements, namely, a reference value, a reflected value and a received value. Each measurement includes amplitude and phase shift.

0014The circuitry connected from the measuring circuit 52 to the transmitter antenna 30 represents a fixed system and has an equivalent circuit configuration. The circuit is altered by the insertion of measuring apparatus. This creates no particular problem because the description sets out a measurement process using the transmission line mismatch exists. The equivalent circuit is a typified two port reciprocal electrical network, and is illustrated in Fig. 2 of the drawings where the network is identified by the numeral 62. In like fashion, the circuitry between the measuring circuit 52 and the receiver antenna 32 has a similar two port reciprocal electrical network representation at 66. The signal transmission path between the antennae 30 and 32 is represented by the circuit 64. Again, it is a two port reciprocal electrical network. It should be kept in mind that the equivalent circuits 62 and 66 are fixed in that they represent the signal transmission system involved in the circuitry of the sonde 10. Because circuitry is fixed, the circuits are therefore two determinable networks. That is, the networks 62 and 66 are fixed and determinable and are represented as the circuitry extending from the respective two antennae. The propagation pathway into the formation 18, is on the exterior of the sensor pad 15 and is variable. When the sonde is at a fixed well depth, a particular two port reciprocal network can then be devised for representation of the strata or formation 18. Since signal propagation through the strata 18 involves electromagnetic signal propagation subject to loss and phase shift, measurements obtained at the measuring circuit 52 are sufficient to enable determination of the equivalent network 64 which is shown in Fig. 2 of the drawings. Returning to Fig. 2 of the drawings, terminal pairs are located at 68, 70, 72 and 74. The measuring circuit 52 in Fig. 1 is connected so that measurements can be made at the terminals 68 and 74. By the use of appropriate short and open circuits connected at and also between the antennae 30 and 32, and by the substitution of microwave signal conductors having matching impedances between the two antennae, measurements can be taken to enable determination of the parameters describing the two port reciprocal electrical networks.

0015The networks 62 and 66 have equivalent circuits which are similar to that shown at 64. Component values are described as S parameters, and all four S parameters are complex impedance at a given frequency. For instance, the network 64 is formed of four equivalent impedances, 76, 78, 80 and 82. Each is represented by real and imaginary components, describing a complex vector. If a short circuit is provided in lieu of the network 64, the values or S parameters for the networks 62 and 66 can be evaluated and then substituted. The values in the networks 62 and 66, once measured and determined, generally are unaltered with use and at a selected frequency.

0016The four S parameters in each of the networks are conveniently identified as S₁₁, S₂₁, S₁₂, and S₂₂ as in the literature, (eg. a paper by Rama N. Rau entitled "Measurement of Core Electrical Parameters at UHF and Microwave Frequencies", SPE 9380. (This paper was presented at the 55th Annual Fall Technical Conference and Exhibition of the Society of Petroleum Engineers of AIME held in Dallas, Texas, U.S.A., September 21-24, 1980.)). The symbol S₁₁ is the S parameter for the circuit component 76 (a complex number). As previously mentioned, the measuring circuit 52 is applied across the terminals 68 and 74. Measurements of incident and reflected signals are made at the terminals 68. These measurements basically define S₁₁ as the ratio of V₆₀ over V₅₀ having a phase angleφ₆₀ minusφ₅₀. The latter angle is defined as the reference, hence is zero, providing the S₁₁ vector with an amplitude of V₆₀/V₅₀ at a phase angle of 0₆₀. The subscripts are the mixer outputs as measured by the measuring circuit 52.

0017Next, the parameter 80 is determined. Since the sonde is raised along the borehole to make repeated measurements, the parameter 80 becomes the parameter 76 when the sonde moves, positioning the transmitter antenna where the receiver antenna is now located. In other words, the sonde is moved along the borehole during routine logging operations so that the transmitter antenna is, at one instant t₁, in the location of the receiver antenna, and at the next instant t₂, it is located as illustrated in Fig. 1. At the time t₁, the transmitter antenna is located at the terminals 74. Since the circuits 62 and 66 are already known because they are fixed values defined by the equipment, the transmitted signal through the terminals 72 can be determined in the same fashion as the prior determination, and the S₂₂ parameter 80 then calculated. Both S₁₁ and S₂₂ are now known.

0018After determination of the electrical parameters 76 and 80, the next step is determination of the values 78 and 82, or "S₁₂" and "S₂₁" as labeled in the literature. As a result of symmetry in the equivalent circuit describing the formation 18, the circuit components 78 and 82 have equal amplitudes given by the ratio V₅₁ over V₅₀. The phase angle is φ₅₄ minus φ₅₀, the latter angle being the reference so that the relative phase angle is φ₅₄. Determination of the four equivalent circuit components is then finished.

0019The next step is to convert the four components from impedance measurements into electrical parameters describing the formation. The desired parameters are formation resistivity, magnetic permeability and dielectric constant. The above referenced SPE article discusses a process of conversion to obtain resistivity, magnetic permeability and the dielectric constant of the formation so that these values are determined for specific formations. All these parameters are useful in log interpretation.

0020Fig. 3 of the drawings is a plot showing propagation constant for the case magnetic permeability is equal to unity, the graph encoding dielectric constant and resistivity. These two are measurable parameters describing the formation 18 along the signal propagation path. This system enables the resistivity and dielectric to be measured in the formation 18, thereby forming an output value.

0021As shown in Fig. 3, measurements of S parameters (amplitude and phase) yield values of dielectric and resistivity. This results from the fact that the measurements made by the measuring circuit are complex variables (meaning vectors having amplitude and phase) which readily convert into the measurement shown in Fig. 3, namely the dielectric constant and resistivity. The measuring circuit 52 provides the necessary amplitude and phase values at the terminals 68 and 74 in Fig. 2 and hence enables determination of the circuit components in the equivalent circuit 64. Dwell time of the tool at the formation 18 may appear substantially nil while the sonde is operated on the fly; however, useful data measurements are obtained at each formation of interest. From the measurements, the dielectric measurement of the materials making up the formation 18 is determined. The repeated measurements taken along the well borehole 14 are used to evaluate the formation 18 and other formations along the borehole.