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Induction logging was originally developed to measure formation resistivities in boreholes containing oil-based muds and in air-drilled boreholes because electrode devices could not work in these nonconductive boreholes. However, because the tools were easy to run and required much less in the way of chart corrections than laterals or normals, induction tools were used in a wide range of borehole salinity soon after their introduction.
Commercial induction tools consist of multiple coil arrays designed to optimize vertical resolution and depth of investigation. However, to illustrate induction-tool fundamentals, it is instructive to first examine the basic building block of multiple-coil arrays, the two-coil sonde.
Fig. 1 shows that a two-coil sonde consists of a transmitter and receiver mounted coaxially on a mandrel. Typical coil separations range from 1 to 10 ft apart. In practice, each coil can consist of from several to 100 or more turns, with the exact number of turns determined by engineering considerations. The operating frequency of commercial induction tools is in the tens to hundreds of kilohertz range, with 20 kHz being the most commonly used frequency before 1990.
The induction transmitter coil is driven by an alternating current that creates a primary magnetic field around the transmitter coil. The primary magnetic field causes eddy currents to flow in a continuous circular distribution (often mistakenly called "ground loops") centered around the borehole axis. The color contours in Fig. 1 show the current distribution. These eddy currents are proportional to the formation conductivity, and they in turn generate a secondary magnetic field, which induces an alternating voltage in the receiver coil. This receiver voltage is first-order proportional to the conductivity of the formation.
Because the transmitter current is alternating, there is a phase shift between the transmitter current and the current density in the formation. This phase shift is not the same in all parts of the formation—it increases with distance into the formation (Fig. 1). Similarly, the phase in the receiver is even further shifted. At very low conductivities, the total phase shift is approximately 180° and increases with increasing formation conductivity. Induction tools have always measured the part of the voltage that is exactly 180° phase-shifted from the transmitter current (called the R-signal). As the conductivity increased, and the phase shifted, the voltage was a bit less than expected from a linear relationship. This difference is called skin effect. Modern induction tools make an additional measurement at a phase shift of 270° from the transmitter current (called the X-signal). These two measurements, being in quadrature, allow precise phase and amplitude measurement of the receiver voltage.
To produce adequate sensitivity to the uninvaded zone, induction tools perforce include signals from a large volume of formation. The challenge is to determine exactly where the measurement is coming from in the formation. Doll defined the geometrical factor as a 2D function g(ρ,z), which defines the part of the total signal that comes from an infinitesimally thin loop around the borehole. This definition is valid only at very low conductivities. Moran defined a modification of the geometrical factor that is valid in low contrast formations at any conductivity. This response is known as the Born response.
The response to formation layers is given by the vertical response function gV(z), which is defined as the integral of the 2D response function g(ρ,z) over radius ρ. The response to radial variations in a thick bed is given by the radial response function gR(ρ), which is defined as the integral of g(ρ,z) over z. The response of the array to invasion in a thick bed is characterized by the integrated radial response GR, which is the cumulative integral of gR(ρ) over radius.
Because the direct transmitter-receiver mutual coupling of a two-coil array can produce a voltage several thousand times that from a formation, two-coil arrays are not practical. The simplest practical array is a three-coil array with a transmitter and two receivers. The second receiver is placed between the transmitter and main receiver, and is wound oppositely so that the voltages in the two receivers exactly cancel when the array is in free space. The response is the sum of the coil-pair responses.
One of the most successful induction arrays was the 6FF40 array introduced in 1960. It had three transmitters and three receivers, with a symmetric Born response g. Figs. 2 and 3 show its vertical and radial responses. The array was designed to achieve deep investigation, reasonable vertical resolution, and a low borehole effect. However, the large peaks in the 2D response along the tool resulted in sensitivity to borehole washouts, called cave effect.
One of the challenges of measuring formation resistivity is to sort out the resistivity of the invaded zone from that of the virgin zone. The earliest concept to successfully solve the problem (at least in thick beds with uncomplicated invasion profiles) was the dual-induction tool. This tool combined a 6FF40 array as a deep-induction measurement (ID or ILD) with a set of receivers that worked with the 6FF40 transmitters to produce a shallower measurement. This was referred to as the medium-depth induction (IM or ILm).
Because there are three parameters in the simplest step-profile invasion model, at least three measurements are required to solve for these parameters. The shallow measurement was a shallow laterolog (LL8 or SFL) colocated with the induction arrays. The radial response function involves very complicated mathematics, and the solution offered to users of the dual induction logs was a graphical solver called the tornado chart.
he ILD-ILM-SFL logs separate when there is invasion, and this separation is what allows interpretation for invasion parameters. Fig 4 shows the modeled response of the dual induction-SFL tool (DIT) in a typical Gulf of Mexico pay zone with a transition over a water zone.
The ILm and ILd measurements do not respond linearly to the formation conductivity. This nonlinearity is closely related to the changes in the response shape and depth of investigation with increasing conductivity. This nonlinear response of an induction array is called skin effect because it is related to the "skin depth" effect of AC current flowing in conductors.
Some sort of function must be applied to the tool voltages to correct for this nonlinearity. The processing applied to the Schlumberger DIT consisted of a skin-effect function ("boost") applied to the measured R-signals from the induction arrays. This was based on computations of the response in an infinite homogeneous medium. The ILd was further processed using a three-station deconvolution filter to slightly sharpen the bed-boundary transition and to correct for shoulder effect over a limited resistivity range (1 to 10 ohm•m). At other formation-resistivity ranges, the response either produced horns or large shoulder effects. Fig. 5 shows the DIT logs in a set of formation layers with the same shoulder-bed contrasts, but centered on 1, 10, and 100 ohm•m.
Borehole correction was also hand-applied to the induction and SFL logs. The borehole correction chart was derived from measurements made with a DIT in plastic pipes full of salt water. The 6FF40-based dual induction-shallow electrode tool was offered by most service companies.
The DIT tool became the standard resistivity tool and remained virtually unchanged for more than 20 years. However, as its application moved from the original Gulf of Mexico formation contrasts to higher-resistivity formations, the shoulder-effect problem became much worse. Although shoulder-correction charts were provided for high resistivity, they mainly indicated that the problem was bad rather than serving as a usable correction mechanism.
The fundamental problem in induction log interpretation is to isolate the response of a thin bed and the virgin zone from the shoulders and the invaded zone after the measurement process has thoroughly mixed them. The Phasor induction tool was introduced in the mid-1980s and was the first tool to automate the environmental corrections. It uses a linear deconvolution function to correct for shoulder effect and uses the X-signal measurement to correct for skin effect. This algorithm was the basis for Phasor Processing. It can be shown that a filter fitted at low conductivity works well at low conductivity but produces large errors at high conductivity. The error is, however, a slowly varying function closely related to the X-signal. An algorithm applied to the X-signal to match it to the skin-effect error allows a single FIR filter to correct for shoulder effect over a wide range of conductivities.
Fig. 6 shows the results of Phasor processing in the formation models of Fig. 5. The induction logs are fully shoulder-effect-corrected at all conductivity levels. Phasor logs in the Gulf of Mexico simulation of Fig. 4 are not very different from the DIT logs. This is in part because this formation is where the DIT logs were designed to work well. Although tornado charts were published for the Phasor induction logs, the invasion parameters are computed in real time at the wellsite. Borehole corrections are based on computer models of an eccentered tool in a wide range of borehole salinities and formation conductivities. Borehole corrections are applied in real time at the wellsite. The Phasor induction tool was the first induction tool that could provide full environmental correction and invasion parameter determination at the wellsite. In 1987, changes to the deconvolution filters allowed induction logs with a 2-ft vertical resolution (compared with 5 ft for ILm and 8 ft for ILd).
Dual-induction tools that measured both R and X signals and applied automatic shoulder-effect corrections were introduced by Atlas (the Dual-Phase Induction Tool, or DPIL) and Gearhart (the High-Resolution Induction Tool, or HRI tool). The HRI tool also achieved a vertical resolution of 2 ft. It was also the first dual-induction tool to be based on a different array from the 6FF40. Its deep array had a median depth of investigation of approximately 90 in. After the breakup of Gearhart, Halliburton acquired the HRI tool and commercialized it.
However, all of these tools are based on two induction arrays—a shallow array and a deep array. Performance in complex invasion profiles is limited by the small number of measurements. Fig. 7 shows the Phasor logs in a simulation taken from a field log in a gas reservoir. Here an annulus has developed, and the deep log reads much less than Rt. In this well, the three-parameter invasion model will not return the correct value of Rt.
In the case of oil-based mud (OBM), the SFL is not usable. Separation between the medium and deep logs is only a qualitative indication of invasion and is not quantitatively interpretable.
With the Phasor Induction tool, the dual-induction concept had reached its limits. In particular, improvements were needed in better estimates of Rt in the presence of deep-invasion or complex transition zones. As the grosser environmental distortions were corrected by Phasor Processing or similar processing, annulus profiles and other transitions were encountered more often.
These response problems, coupled with an increasing use of OBM, led to the concept of using several induction arrays with different depths of investigation. With the problems of applying linear deconvolution filters solved, then Doll’s approach of using a simple array was applicable. The Schlumberger AIT was designed with eight simple three-coil arrays ranging in length from 6 in. to 6 ft.
The first step in log formation in the AIT family of tools is to correct all raw array signals for borehole effects. This process is based on a forward model of the arrays in a circular borehole, and it includes an exact description of the tool in the model.
The signal measured by an induction sonde eccentered in a borehole can be described mathematically as a function of four parameters. These are the borehole radius r, the mud conductivity σm, the formation conductivity σf, and the tool position x with respect to the borehole wall (commonly referred to as the "standoff").
The correction algorithm is designed to solve for some of these parameters by minimizing the difference between the modeled and actual logs from the four shortest arrays. The information content of these measurements is not sufficient to solve for all the borehole parameters at the same time. In practice, two of the four parameters can be reliably determined by this method. The other two parameters have to be either measured or fixed. The equivalent homogeneous formation conductivity σf must always be solved for because no measurement is closely enough related to it. This leaves one of the other parameters to be determined, and the remaining two parameters must be entered as measurements. This leads to the three borehole correction methods to compute mud resistivity, hole diameter, and standoff. All of the AITs except the original AIT-B have integral mud resistivity sensors, and "compute standoff" is the default borehole-correction method in water-based mud (WBM).
A method was developed to combine these array measurements to focus the resulting log to the desired depth of investigation, while at the same time doing so with a high vertical resolution and minimizing cave effect. The log-formation process is described by the equation
In this equation, σlog is the recorded AIT log, σa(n) is the measured log from the nth channel, and N is the total number of measure channels. This process produces a log that is different from that produced by any of the individual arrays. It is still characterized by a response function. This response function is a weighted sum of the response functions of each of the individual channels n. Skin effect is handled in a manner similar to the Phasor tool.
The result of this equation is a combination of the logs from the eight array that "distills" the radial information from the eight arrays into five independent logs with depths of investigation of 10, 20, 30, 60, and 90 in. Each of these five logs is available at a resolution of 1, 2, and 4 ft. The radial profile is identical at all resolutions, and the vertical resolution is identical for all radial depths. The set of weights w in Eq. 1 determines which log is produced.
If the mud is very salty, or if the borehole is very large, the signal in the AIT arrays from the borehole will be very large. With salty mud, even normal variations in the borehole surface from the drilling operation can cause "wiggles" on the short array data. Several years of practice have shown that these can affect the final logs, especially the 1-ft logs. This experience has shown that in an 8-in. borehole with 1 1/2-in. standoffs, the 1-ft logs are normally usable at Rt/Rm contrasts up to 100; the 2-ft logs are usable up to a contrast of 450, and the 4-ft logs are usable up to contrasts of 1000. Algorithms based on the real-time use of a chart and "road-noise" analysis of the 6-in. array allow real-time selection of the appropriate resolution based on actual logging conditions.
AIT logs separate in invaded zones and give a good visual indication of invasion, even with OBM. Fig. 8 shows the AIT logs in the same formation as Fig. 4 (left). In the annulus case, Fig. 8 (right), the AIT logs are "out of order," clearly indicating the nonstep nature of the invasion profile.
With the additional curves, the invasion profile parameters can be solved for using inverse methods. AIT invasion processing has three models that can be selected:
All are available at the computing center, while the ramp profile is used for real-time logs.
Interpretation of logs in deviated wells or where the apparent dip is high is considerably complicated. First, one has to recognize that the logs are at high apparent dip. Fig. 8 shows AIT logs in a formation with an apparent dip of 85°. Although this is high, the characteristics that appear here—horns and strange log order—appear in logs with dips as low as 40°. In many fields, faults and slumping of young sediments can produce high apparent dips that are not detectable on seismic profiles. Merlin processing has been developed to produce logs fully corrected for dip effect. Recently, real-time high-angle processing was made available. This processing produces logs that are independent of dip angle. However, the resulting logs are also shallow. Fig. 9 shows dip-invariant processing (Grimaldi) on the right.
Users of induction logs should be very careful making quantitative analyses in wells that are deviated, or if the formation is dipping. If the shoulder-bed contrast is 20 or less, then the minimum angle where dip correction is needed is approximately 30°. At shoulder-bed contrast of over 100, the logs will need correction at dips as low as 10°.
A few field-log examples will illustrate the richness of information available in array-induction logs. The first example, Fig. 10, is a comparison of AIT and Phasor induction logs in a gas zone from Canada. The AIT shows a nonmonotonic curve order, indicating an annulus profile. If the data from this zone is inverted into an annulus profile using material-balance constraints to determine the thickness of the annulus, then the complete annulus parameters can be recovered (Fig. 11).
The next example is from south Texas, and is in a well drilled with oil-based mud. Fig. 12 shows the AIT logs compared to the Phasor logs in this well. Because of the OBM, only the induction logs from the DIT are available. In the lower zone, the AIT logs show a conductive invasion profile, suggesting that the OBM has broken down as it has invaded into the formation. The invasion profile is much clearer with the AIT logs.
The final example is from a deviated well in Canada in a 4 3/4-in. borehole drilled with OBM (Fig. 13). The well was air-drilled and turned horizontal. This part was at a deviation of approximately 60°—going "round the bend." The 2-ft field logs in the left track have a scrambled curve order—shallow logs are higher than deep in the resistive beds and then reversed in the conductive beds. This is a signature of high-dip response. The dip-invariant logs in the center track do not exhibit the curve scrambling. The Merlin logs also show no scrambling and high resolution as well.
Other array induction of tools
Baker Atlas introduced its High-Definition Induction Log (HDIL) array induction tool in 1996. It is a seven-array tool that operates at eight frequencies. This information can be processed in a variety of ways, depending on the environment. The multiple frequencies are used for skin-effect correction. This algorithm is developed by computing the R signal measured by a given array at each frequency at a wide range of formation conductivities. The data at each frequency are fitted to the true formation conductivity. The resulting function is used for the skin-effect correction.
The skin-effect-corrected conductivities are then deconvolved with filters to form six logs at depths of 10, 20, 30, 60, 90, and 120 in., and at three matched resolutions of 1, 2, and 4 ft. An additional presentation is the "true resolution" log set. This has the same six depths, but the resolution of each depends on the depth of investigation. This presents the resolution information content that actually comes from the formation region near the midpoint of the integrated radial response function. Dip correction is provided at the computing center. Fig. 14 shows an example. Fig. 15 shows a 2D inversion available at the computing center.
Halliburton introduced its High-Resolution Array Induction (HRAI) tool in 2000. It is a six-array tool based on the array layout of the HRI. Standard HRAI tool logs present resistivities at vertical resolutions of 4, 2, and 1 ft, each with six depths of investigation (10, 20, 30, 60, 90, and 120 in.). The log resistivities are inverted to yield true resistivities of the formation in the virgin zone, Rt, and in the invaded zone, Rxo, near the borehole. Invasion diameters (Di) corresponding with Rt and Rxo are also presented. HRAI tool answer products are available in real time while logging.
A variant on the array induction principle was introduced by Weatherlord (previously Reeves Wireline). The array induction donde (AIS) combines four simple induction arrays with a shallow focused-electrode array. The induction data have been presented in two ways. Originally, the four arrays were combined in software to match the response of the ILd and ILm arrays. Later, the Vectar processing was introduced to produce a higher-resolution log. Data from each array is skin-effect-corrected and then resolution-matched to the shortest array. Up to six curves are presented from the four arrays.
Induction vs. laterolog measurements
Laterolog and induction logging tools each have unique characteristics that favor their use in specific situations and applications.
The induction log is generally recommended for holes drilled with only moderately conductive drilling muds or nonconductive muds (e.g., oil-based mud (OBM)) and for empty or air-drilled holes. The laterolog is generally recommended for holes drilled with very conductive drilling muds (i.e., salt muds).
Induction tools are conductivity-sensitive devices, which are most accurate in low- to medium-resistivity formations. Laterolog tools are resistivity devices, which are most accurate in medium- to high-resistivity formations. In practice, both modern laterolog and induction-logging tools are suitable for most logging conditions, and it is no longer practical to make a specific recommendation for one type in preference to the other, except in extreme conditions.
Laterolog devices see the more resistive zones, and induction tools see the more conductive zones. Therefore, when Rxo is greater than Rt, an induction tool is preferred for Rt determination because laterolog tools will be affected mostly by Rxo. Conversely, a laterolog tool is preferred when Rxo is less than Rt. Conductivity in the borehole has a strong influence on an induction measurement, but little influence on a laterolog measurement.
Starting with the Phasor Induction tool, borehole-corrected logs for induction tools have been available at the wellsite. A caliper and estimate of mud resistivity is essential for induction-borehole correction, either by hand using a chart or automatically.
The array induction imager tools (AITs) have only automatic borehole correction—no charts exist. An analytic forward model was used to compute thousands of cases for the AIT covering the range of each of these parameters. At the wellsite, a caliper and accurate measurement of Rm are used as inputs, and the other two parameters are solved for in a least-squares inversion through the computed table. This method is essential to produce an accurate 10-in. log over a wide range of borehole sizes and mud resistivities.
The following are guidelines for running induction logs, especially array-induction tools:
- A caliper is required in the same toolstring as the induction tool.
- Rm must be measured adequately, preferably downhole, using an accurate sensor. There can be large errors in values of mud resistivity based on surface measurements.
- Adequate standoff is essential. Never run slick.
If these guidelines are followed, modern AITs can give accurate estimates of Rt even when Rxo/Rt is as low as 0.2.
The high-resolution laterolog array (HRLA) tool with its inversion of the five array logs has extended the usability of laterolog tools further into the Rxo > Rt region. The AITs, again with inversion of the logs, have extended the induction range in the Rxo < Rt region. Fig. 16 shows the range of usability of the AIT and HRLA tools. In the broad overlap region, both tools can be used. In this region, the HRLA array laterolog tool can be combined with the AIT to determine anisotropic resistivity— Rv and Rh in vertical wells.
When looking at both induction and laterolog logs from the same well or the same field, do not expect the logs to overlay. The Rt values for both tools should be close, but the logs themselves, uncorrected for environmental effects, can be quite different.
When working with older logs, one must keep in mind that both laterolog and induction measurements are influenced by the borehole and by surrounding beds. Surprisingly, thick beds may have some effect on their measurements, depending on shoulder-bed contrast. The measurements of both devices should always be corrected for borehole and surrounding bed effects. Although these corrections are in many cases small, it is good practice to make them routinely. This will ensure that they are not overlooked in the larger number of cases where they are significant.
With either laterolog or induction deep-resistivity measurements, it is essential to record at least three resistivity-log curves with different depths of investigation. With fewer than three competent measurements, it is not possible to make an estimate of the invasion parameters, and Rt and Rxo become guesses. Array-induction and array-laterolog tools make a sufficient number of measurements to use the more rigorous inversion solutions, deriving even more reliable values of Rt and Rxo.
|amf||=||mud filtrate chemical activity|
|aw||=||formation water chemical activity|
|di||=||diameter of invasion (in., m)|
|G||=||induction integrated radial-response function|
|I||=||electrical current, Amperes|
|Rann||=||resistivity of the annulus|
|Rh||=||resistivity in the horizontal direction (ohm•m)|
|Rm||=||resistivity of the mud column (ohm•m)|
|Rmc||=||resistivity of the mudcake|
|Rmf||=||resistivity of the mud filtrate|
|Rxo||=||resistivity of the invaded zone|
|Rt||=||resistivity of the uninvaded formation|
|Rv||=||resistivity in the vertical direction (ohm•m)|
|Rw||=||resistivity of the formation connate water (ohm•m)|
|Rwa||=||apparent water resistivity from deep resistivity and porosity|
|Sxo||=||water saturation of the invaded zone|
|Sw||=||water saturation in the uninvaded zone|
|t||=||acoustic travel time (μs/ft)|
|tma||=||acoustic travel time of the rock matrix(μs/ft)|
|V||=||electrical voltage, volts|
|Vsd||=||fraction of the total formation volume that is sand|
|Vsh||=||fraction of the total formation volume that is shale|
|ρma||=||density of the rock matrix|
|σm||=||conductivity of the mud column, mS/m|
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- Kienitz, C. et al. 1986. Accurate Logging in Large Boreholes. Paper III presented at the 1986 SPWLA Annual Logging Symposium, Houston, 9–13 June.
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