MXPA98001274A - Method and apparatus to measure the density of a formation and the photoelectric factor of the formation by an instrument with various gamma-ga ray detectors - Google Patents

Abstract

The present invention relates to an improved method and instrument for determining the density of a formation using a series of gamma-ray detectors. This invention can correct the considerable separations found in irregularly shaped sounding wells and, in particular, the larger separations typically found by mandrel-like instruments. In this invention, collimated detectors have varying depths of investigation within the formation. In small separations, a short distance detector (DC) mainly investigates mud and mud scale and a surface layer of the formation. Unlike the DC detector, a medium distance detector (DM) has a greater depth of investigation and is sensitive to borehole and formation, even in the case of larger separations. A long distance detector (DL) is sensitive mainly to the density of the formation and its reading of the density is corrected using the information of the separation of the DM and DC detectors. In addition to measuring the density, this invention can measure the photoelectric factor (FFE) of the array. Since the photoelectric absorption preferably eliminates the minimum energy gamma rays, the housing of the instrument must allow the passage of minimum energy gamma rays. This is achieved by using a window composed of a material with low atomic number (Z) or by using a material for housing low Z such as titanium. The typical materials of the windows are beryllium and titanium. Housing materials can be titanium or, for low pressure requirements, graphite or high resistance carbon composites

Description

METHOD AND APPARATUS FOR MEASURING THE DENSITY OF A TRAINING AND THE PHOTOELECTRIC FACTOR OF THE TRAINING THROUGH AN INSTRUMENT WITH SEVERAL GAMMA-GAMMA RAY DETECTORS FIELD OF THE INVENTION This invention is related to the determination of the density and lithology of a geological formation. In particular, it is related to the determination of the density of the formation using a set of three detectors that allow to measure the densities of the formation, even at a wide distance between the apparatus and the formation, and which measure the photoelectric factor of the formation.

DATA OF THE INVENTION Nuclear instruments have been used for decades to determine the density of the rocky geological formations surrounding a borehole. The instruments for measuring nuclear density depend on the Compton scattering of the gamma rays in the formation to perform the density measurements. A conventional density measuring instrument consists of a gamma-ray source (or X-ray), at least one gamma-ray detector and shielding between the detector and the source, in order to detect only the scattered gamma rays. . During density -diagraphy, gamma rays from the instrument's source travel through the borehole into the geological formation. The gamma rays will be scattered by the electrons in the formation or well and some of them will be scattered back to the detector in the logging probe. Depending on the space between the source and the detector, the speed of counting of detected gamma rays will increase with the increase in the density of the formation (dominant dispersion term) or decrease with the increase in the density of the formation (effect predominantly nurturing). In intermediate spaces, both the terms of attenuation and dispersion affect the response. In an ideal situation, the well would have a uniform and straight shape. This uniform borehole would allow a density measuring instrument equipped with a detector to be in close proximity to the formation surrounding the well and the separation of the instrument would be minimal. Under these conditions, a detector would be sufficient to perform the density measurement. However, since boreholes usually do not have a uniform shape and are not straight, an important problem in performing the density log is the contact of the borehole with the wall of the borehole. Density density probes can be designed as cushion or mandrel type instruments. In a mandrel, the source and detectors are in the body - of the straight cylindrical instrument. The rigid length of such an arrangement makes it difficult for the instrument to keep in close contact with the wall of a non-uniform borehole. In the cushion-type instruments, the detectors and, in many cases, also the source of the graph are mounted on a short and articulated cushion that can be moved relative to the body of the instrument. A strong decentralizing arm pushes the cushion against it. Well bore wall allowing better contact thanks to the shorter length of the dis positive. All density density probes will find a mud crust, accumulated in the wall of the formation, which prevents good contact. The density measurement needs to be compensated also for this type of separation. Due to the imperfections of mandrel-type instruments, they are used only if a cushion-type instrument can not be designed due to size or cost constraints. Most modern density measurement instruments use an articulated cushion that contains the detectors and the gamma ray source. A backup arm pushes the cushion against the formation. The small length of the cushion and the great decentralization force exerted by the - - Backrest arm ensures excellent cushion contact - with training in most cases. However, for tools with a smaller diameter, the use of a cushion construction becomes difficult or impossible. In these cases, the detectors are placed inside the housing of the instrument (mandrel-type instrument). Decentralization is provided by an arc spring and / or a calibration device with a backup arm. However, the greater length and rigidity of the instrument results in a lower quality application of the instrument to the borehole wall and requires a higher than normal separation. The basic design of a two-detector instrument is shown in Figure 1. Instrument 1 consists of a gamma-ray source 2, a short-distance detector (DC) 3 and a long-distance detector (DL) 4. The instrument is in a borehole 5 that is substantially uniform. The gamma rays emitted by source 2 are introduced into the borehole and formation 6, where they are scattered and some are then detected by the detectors. The DC 3 detector is more sensitive to the region near the instrument 7. The DL 4 detector detects the gamma rays 8 of the formation 6 at a greater depth than the DC detector and is less sensitive to the effects of the separation of the instrument. The bulk density derived from the measurement of - - - DL detector can be corrected for the separation of the instrument by comparing the readings of the apparent density of the DL and'DC detectors. The correction for the separation caused by the accumulation of the mud scale or separation of the instrument can be achieved by using two detectors with different depths of investigation. In this case, the first detector (DC) has little depth of investigation and is more sensitive to the fluid in the borehole or to the mud scale between the instrument and the formation. A second detector - (DL) at a greater distance from the source is less sensitive to the environment of the well and more sensitive to formation. The difference between the readings of the two detectors can be transformed into a correction for the separation and the crust of lo-do. However, in the case of larger separations, the compensation of the 2 detectors is often insufficient or ambiguous. The inaccuracies of the measurement with two detectors reside in the fact that the measurement of two detectors is used to determine three unknowns: the density of the for-macidn, the separation (distance between the instrument and the -wall of the well) and the density of the fluid and / or mud scale between the instrument and the formation. With small separations, the last two unknowns can be combined in an effective thickness (separation of mud density). Even greater separations, this approach fails and the corree - - Cidn becomes ambiguous. Also, the depth of investigation of the short distance detector may become smaller than the separation. This will avoid a proper compensation. The situation of a large separation is illustrated in Figure 2. The. instrument of two detectors 1 is in the borehole 5. Due to the irregu- lar shape of the borehole wall 9 the instrument is separated from the wall by a considerable distance. The depth of investigation of the short distance detector 3 is-less than the separation and achieving effective compensation-of the density response of the long distance detector 4 is more difficult and, sometimes, impossible. The use of an additional detector located between traditional DL and DC detectors can help to deal with the ambiguity of the correction before a considerable separation of the instrument and some of the limitations of the instrument of two detectors can be overcome. The measurement of three detectors provides the ability to distinguish the effect produced by the thickness of the mud and / or mud crust from the effect produced by the density of the mud and / or mud scale between the instrument and the formation. Also, the best statistical accuracy provided by the average measurement will improve the speed of the probe's image. The operation of the three detector instrument is shown in Figure 3.

- - The instrument of three detectors 11 has the capacity to -measure three depths of investigation different in the -formation. The instrument has a source 12, and short distance detectors (DC) 13, medium distance (DM) 14 and long distance (DL) 15. The idea of using three detectors to differentiate -different depths of investigation was described in U.S. Pat. 4,129,777 (ahl). In ahl, the main idea is to measure the density of the material in three different depths of the instrument. This can be used to determine the density of the formation through the casing, to determine the thickness of the cement behind the casing or to determine the density and thickness of the mud scale between the instrument and the - training. In all three cases, the measurement is also used to determine the density of the formation and the thickness and density of the layer of material between the instrument and the shape. In Wahl, gamma radiation is emitted from the instrument into the surrounding medium, and the measurements correspond to the amount of radiation that returns to the detectors as a result of the radiation interaction - emitted with the first, second and third radiation. , layer respectively of the surrounding medium, each of them starting in the borehole and extending to the increasing radial depths. These measurements are taken by three detectors located at different distances from the gamma radiation source in order to have three different depths of investigation. A representation of the thickness of the solid material is then obtained from the three measurements of gamma radiation. Specifically, the method proposed by Wahl is useful for determining the thickness of the material bound between the borehole of the borehole and the adjacent adjacent formation. In this case, the three measurements of the gamma radiation (superficial, intermediate and deep) are corrected for the attenuating effect of the coating. Thus, three densities are calculated from the radiation measurements-superficial, intermediate and deep respectively. Another patent that incorporates the concept of three detectors is the US patent. UU 5,525,797, Moake. In this patent, as in the Wahl, the source of gamma rays is axially separated from the first, second and third detector. The first / near detector is axially separated from the gamma-ray source by a distance defined as a -first separation. The first separation and collimation for the first detector are designed in such a way that the gamma rays detected in the first detector are the gamma rays scattered mainly by the coating. The second or half detector is axially separated - distance from the gamma ray source than the first detector. The second detector is separated from the source of gamma rays by a distance defined as second stop. The second separation and collimation for the second detector have been designed in such a way that the gamma rays detected in the second detector will be those scattered mainly by the coating and the cement. Finally, the third detector or far detector is separated -axially at a greater distance from the source of gamma rays than the first and second detectors, by a distance defined as a third separation. The third separation and collimation defined by the third detector have been designed in such a way that the gamma rays detected in the third detector are those scattered mainly from the coating, cement and formation. It is this third detector that allows the instrument to measure the density of the formation after the first and second detectors allow mainly -the instrument to compensate for the coating and the cement. However, the second detector can be used to measure the density of the formation in the absence of cement. Preferably, the detectors are protected - by a high density material, between the source and the detector, which prevents the detection of gamma rays that simply - move through the instrument. A gap or vacuum is provided in the collimation channel-like shield extending from the detector through the instrument and ending outside the surface of the instrument. The collimation channels are designed specifically for the detection scheme of each detector. Specifically, the first detector or nearby detector will have a collimation directed at a small angle with respect to the coating so that the first detector will detect the gamma rays scattered mainly by the coating. The second detector or medium detector will have a collimation -directed at a more inclined or perpendicular angle with respect to the coating because the second detector has the function of detecting gamma rays dispersed throughout the cement, in addition to the coating (greater depth of investigation) . Finally, the third detector or detector will have a large collimation channel that is directed substantially perpendicular to the cladding due to the distance to which the third detector of the source is located. Since the gamma rays detected in the far detector must pass to. Through the coating, cement, formation, before passing back through the cement and coating, the statistical probability that this event occurs is less than for the first and second detectors and, therefore, a channel is required. Colima Cidn wider for the third detector. The density of the three detectors presented by - - Wahl describes the general idea of using three detectors to measure density in the presence of a material of substantial thickness and / or density between the instrument and the formation. The distinction between the different depth of investigation is achieved by the different axial separation of the detectors. The invention presented by Moake uses substantially the same detector separations as the -Wahl invention. The detector's collimation is optimized for a measurement through the casing. The detectors DC (first) and DL (third) use a collimation very similar to that used in the traditional density instruments of two detectors. The DM detector (medium) collimation is very accurate and almost perpendicular to the borehole wall to obtain a deeper density reading in measurements through the coating. The pronounced collimation angle of the DM detector reduces its counting speed and statistical precision. In an openhole measurement the depth of investigation of the DM and DL detectors will be very similar and the sensitivity to the mud scale, which has a lower density than the steel coating, will be reduced. This still requires a solution to determine compensation of separation in the diagnostic probes that can overcome these limitations. The present invention provides a measurement of several detectors optimized for situations where a density measuring instrument finds a substantial separation of the formation. In spite of being optimized for open-well logging, the -instrument can also be used in well-closed logs. In order to achieve this goal, the instrument uses a set of optimized collimators for short, medium and long distance detectors. In particular, the collimation of the average detector is different from the collimations of the short or long distance detectors. This provides the correct depth of investigation for the average detector, that is, an intermediate depth of investigation between the short and long distance detectors. In addition, this type of collimation is very suitable to perform a high precision density measurement and to perform an optimized measurement of the photoelectric effect. In addition to measuring density, most modern nuclear density instruments also measure the photoelectric factor (FFE) of the formation. This measurement depends on the absorption of minimum energy gamma rays through the photoelectric effect in the formation. Since the photoelectric effect depends vastly on the atomic number - of the elements of the formation, it will provide an indication of the formation's lithology. Because the photoelectric absorption preferably eliminates the gamma-rays of minimum energy, the housing of the instrument must allow the passage of the minimum energy gamma rays to the detectors inside the housing. This objective can be achieved by using a window composed of a material with a low atomic number (Z) in the housing or by using a low Z material in the housing, such as titanium. The typical materials of the window are beryllium and titanium. The housing materials may be titanium or, for low pressure requirements, graphite or high-strength carbon composites.

SUMMARY OF THE INVENTION The object of this invention is to provide an optimized means for performing a density measurement of high quality in the presence of a considerable separation -of the instrument. Another objective of this invention is to provide a thinner logging probe (mandrel) with a measurement quality that is at least as good as that of the traditional cushion-type instruments with two detectors. Another object of this invention is to provide an improved means for detecting the photoelectric effect of a geological formation. Another objective of this instrument is to provide a photoelectric measurement of two or three compensated detectors - - for separation. This invention is an improved method and instrument for determining the density of the array using a series of gamma-ray detectors. This instrument has - improved separation correction, better precision and significantly improved measurement for the photoelectric effect. Likewise, this instrument has a smaller diameter than that of conventional diagnostic probes. This invention can correct considerable gaps in sounding wells in an abnormal manner and in particular the large gaps typically found by mandrel-like instruments. During operation, three or more collimated detectors detect the gamma rays emitted by the instrument's source. According to the design of the detector, the detectors have different depths of investigation in the training. In small separations the DC detector mainly investigates the mud and the mud crust and the surface layer of the formation. As the separation increases, the DC detector signal is no longer sensory to the formation or to the sludge or mud crust that is in close proximity to the formation. The DM detector has a greater depth of investigation and is sensitive to the well of sounding and training even in the event of greater separation of the instrument. The long distance detector (DL) is mainly sensitive to the density of the formation. The - - - DL density reading is corrected using information from the DM and DC detectors to provide a more accurate density reading. This invention is also an improved method for de-terminating the photoelectric factor (FFE) of the array. The use of a set of three detectors in a titanium housing provides a high-quality FFE response, more accurate and accurate than that of traditional two-detector instruments, despite the fact that the reduced diameter of the instrument does not allow windows to be used. with low Z for minimum energy gamma rays.

BRIEF DESCRIPTION OF THE DRAWINGS FIGURE 1 is a diagram of a diagnostic probe that detects gamma rays using two detectors. FIGURE 2 is a diagram of a two-detector logging probe in the case of a large-size separation caused by the irregular shape of the borehole. FIGURE 3 is a view of the detection by three gamma ray detectors dispersed in the borehole and formation. FIGURE 4 is a schematic view of the density measurement instrument implemented in the current invention.

- - FIGURE 5 is a diagram of the detection of signals using the current invention in an irregular borehole. FIGURE 6 is a diagram of the detector collimation in a diagnostic probe that implements the present invention. FIGURE 7 is a diagram of the detector section of a diagnostic probe implemented in the current invention. FIGURE 8a is a cross-sectional view of the collimation of the short distance detector. FIGURE 8b is a cross-sectional view of the collimation of a possible medium detector. FIGURE 8c shows an alternative collimation of the detector. FIGURE 8d is a cross-sectional view of a collimation with a possible remote detector. FIGURE 8e shows a collimation of the alternative laser detector.

DETAILED DESCRIPTION OF THE INVENTION The basic arrangement of the instrument is shown in Figure 4. The instrument consists of two sections: a -section with a probe 20 with detectors 13, 14 and 15 and a section with the source of gamma 12 and electronic 21 with -los nuclear amplifiers, digital analog converters and auxiliary circuits for the operation of the instrument. Despite the fact that the figure shows a mandrill type instrument, the design of the. probe can be implemented in a cushion-type instrument. Figure 5 shows the implementation of the current invention in a borehole where there is a large separation from the well wall. Due to the shape of the wall of the well 9 a considerable separation 23 occurs between the instrument 11 and the sounding wall 9. To overcome this separation, some detectors must have depths of investigation superior to the separation of the instrument. The detectors 14 and 15 have depths of investigation, 25 and 26 respectively, which extend into the interior of the formation 6 and allow the measurement of the formation. Figure 6 shows the current invention in an irregular borehole with collimating detectors. The collimation of the gamma ray source and the detectors is optimized to ensure that all detectors have a different research depth in order to improve separation compensation. Likewise, collimation ensures that the instrument is sensitive mainly to the gamma-rays scattered in the formation or region between the instrument and the formation, accepting only the incident gamma rays from a particular direction. The source of ra - yos gamma is also collimated, to cause the gamma rays to be emitted preferably within the formation and to reduce the number of gamma rays moving in the borehole. As shown, the collimation angle 30 for the short distance detector 13 detects the gamma rays in the borehole and in surface depths of the formation. The collimation angle 31 for the detector-mean 14 captures the gamma rays that travel through the formation, in addition to the gamma rays that move through the borehole. The angle of collimation 32 for the long distance detector 15 captures the gamma rays that travel through the formation at substantial depths, in addition to some gamma rays from the sounding well. Figure 7 shows a schematic cross-section through the portion of the probe. The section contains the gamma-ray source 12 and three (3) gamma-ray detectors 13, 14 and 15 to detect the gamma rays. The source of gamma rays may be a traditional chemical source (Cs, Co, or another radionuclide) or an electronic source (X-ray tube, betatron, or other X-ray generating device). The gamma-ray detectors may be scintillation detectors (Nal, GSO or other scintillation materials) coupled to photomultipliers or other amplification devices. For some applications, it may be preferable to use semi-detectors. drivers or other detection devices. In the current invention, the preferred gamma ray source is Cs and the gamma ray detection is preferably performed by scintillation probes Nal and GSO. The collimation of the gamma ray source and detectors is optimized to ensure that all detectors have a different depth of investigation in order to improve separation compensation. In this invention, the actual separation of the detectors, and in particular the separation of the collimation slots from the source, will influence the depth of investigation of the gamma rays detected by each detector. The short-distance detector 13 has a separation of between 4 inches (10.16 centimeters) and 7 inches (17.78 centimeters) from the source 12. The medium detector 14 has a separation of approximately 7 inches (17.78 centimeters) ) and 12 inches (30.48 centimeters) from the source. The long distance detector 15 has a spacing of approximately 12 inches (30.48 centimeters) and 18 inches (45.72 centimeters) from the source. This separation refers to the vertical distance between the center of the source and the center of the detector. It is recommended that the collimation angle 30a for the short distance detector be 30 ° to 60 °. The forward collimation angle of the average distance detector 31a should be 35 ° to 90 °. The forward collimation angle of the long distance detector 32a, shown in Figure 7, is between 45 ° and 90 °. Referring to Figure 8a, the opening of the short-distance detector collimator 40 is generally a cylindrical or elliptical orifice subtending an angle between + 5 ° and + 20 °. As shown in Figure 8b, the azimuthal aperture of the average distance 41 ranges from + 10 ° to +35 ° C. Figure 8c shows an alternative aperture 42 of the medium distance detector The aperture of the long distance collimator 43 shown in FIG. Figure 8d is between + 20 ° and + 50 ° Figure 8e shows an -alternative opening 44 of the long distance detector 15. The azimuthal angles of the collimator are of short distance • medium < long. providing an improved means of detecting the photoelectric effect of a geological formation is also affected by the detector's collimation.This objective is achieved as shown in Figure 7. The gamma-ray source 12 is protected and collimated by a 33 filer for obtaining a preferred gamma-ray emission towards the formation. In front of the source a window 34 of low density material is placed in order to raise to the maximum the number of primary gamma rays emitted into the interior of the formation. The source is also collimated in such a way that the gamma rays are emitted at an angle that improves the ability to disperse them towards the detectors through an opening on the side of the collimator of the source 35. The source is also protected in such a way that The number of gamma rays emitted by the source into the borehole is minimized. This is achieved by a cylindrical bulge around the source and a thick shield behind the source. In Figure 7 the short distance detector is designed to be sensitive to the separation of the instrument., minimizing the azimuthal opening of the detector, as seen in illustration 40, in Figure 8, and orienting the collimation 30a at an angle directed toward the source. The average distance detector 14 is collimated to improve the sensitivity of the training at the same time - which remains sensitive to the region of separation between the instrument and the formation. The optimization of the collimation of the average distance detector can also improve the response of the detector to the photoelectric effect. The collimation of the long distance detector 15 leads to a higher-depth investigation. Also, by opening the collimator of the long-distance detector azimutially, the counting rates are increased at the same time that the signal from the borehole is kept small. The detectors may be Nal scintillators or, preferably, GSO scintillators or other dense and rapid scintillation materials. The short distance detector - - Preferred is a GSO detector. The use of GSO allows the best protection and collimation in a small instrument and its high counting speed makes it the perfect instrument for the high counting speeds found in the short distance detector. The use of very compact integral detectors reduces the length of the -detector and allows a narrow separation. The detector housings are composed of a high-permeability magnetic material that provides protection against magnetic fields. A window in the detector housing reduces to a minimum the attenuation of the gamma rays that enter - through the collimation in front of the detector. The protective and collimation material is generally a dense material with a high atomic number (ie, tungsten, lead or uranium). The gamma rays moving towards the detector can cause the emission of X-rays by the protection material, which can be detected by the detector. X-rays deteriorate the response to the photoelectric effect. They are suppressed by protecting the back of the tector by a 0.5 to 2 mm layer of intermediate Z material (Z = 30 to 60) that absorbs unwanted X-rays and at the same time does not emit X-rays in the range of energies used for measurement. The shielding can be inserted between the detectors to prevent the gamma rays entering through the opening of the collimator from moving to the next detector after dispersing in the first. The algorithms for density and FFE can be of the "column and rib" type as described in the Case and Ellis patents. Other algorithms can be progressive and investment models or the use of weighted multiple linear regression. The collimation of the medium and long distance detectors makes the instrument suitable for a compensated measurement of the photoelectric effect - (under evaluation) in the presence of sludge containing -materials with a high atomic number and, therefore, - They exhibit a wide photoelectric effect. The apparatus and method of this invention provides significant advantages compared to current devices. This invention has been described in connection with the preferred physical representation. However, it is not limited to it. Changes, variations and modifications can be made to the basic design without deviating from the inventive concepts in this invention. Also, these changes, variations and modifications will be evident to the design experts who will have the advantage of the preceding descriptions. Tales changes, variations and modifications must abide by the terms of the invention which is limited only by the following claims.

Claims (3)

1. An apparatus for determining the characteristics of a geological formation around a borehole and comprising: (a) a source for irradiating such a -geological formation with gamma rays; (b) short, medium and long distance detectors located in said apparatus, respectively, at fixed distances, successively greater, of said gamma-ray source, and said detectors being capable of generating signals indicating the energy of the radiation ga mma detected by each of the detectors; Ce) a housing containing said source of gamma radiation and detectors, and said source being able to retain its mechanical properties in hostile environments in a borehole? Cd) a means for calculating the density of the formation from the signals of said detector; and (e) a means for calculating the photoelectric factor of said geological formation from the signals of said detector.

2. The apparatus of claim 1, wherein each of said first, second and third detectors are collimated exclusively in such a manner that each detector detects gamma rays from different depth ranges.

3. The apparatus of claim 1, wherein said short, medium and long distance detectors have different depths of investigation inside the - - formation, and where said depths of investigation increase with the distance of the detector from said source of gamma rays. 4, The apparatus of claim 1, further comprising a shielding between the source and the detectors to prevent gamma rays from moving directly from the source to the detectors and shielding around parts of said detectors to protect them. against gamma radiation scattered in the borehole. The apparatus of claim 2, wherein said source of gamma radiation is collimated so that the gamma radiation emitted by said source within said cynid form is preferably directed into the formation at an angle such that it improves dispersion towards the de-tectors in the instrument. 6. A method for determining the characteristics of a geological formation around a borehole -which includes the following steps: (a) collimation of a radiation source and short, medium, and long distance detectors, in such a way that the The radiation emitted by said source into said formation is preferably directed to the interior of the formation and at an angle that improves the dispersion toward the radiation detectors placed in said probing well at progressively greater distances from said radiation source. (b) irradiation of said for - 6 - macidn with gamma rays from said source of radiation; (c) generation of a gamma-ray spectrum from the gamma rays detected in each of said detectors; (d) calculation of an apparent density from the spectrum in each detector; and (e) measurement of a photoelectric effect from the spectrum of each detector. 7. The method of claim 6, which also comprises the step of calculating the distance of the separation between an apparatus containing said detectors and the source and the wall of such borehole from the spectrum of the three detectors. The method of claim 7, which also comprises the step of compensating said photoelectric effect to account for the separation of said apparatus. 9. The method of claim 7, wherein the density of said formation, separation and photoelectric effect of the formation are calculated from a progressive pattern of density, separation and photoelectric effect and subsequent inversion of the progressive model. 10. The method of claim 6, which also comprises, before step (e), the step of optimizing the co limation of the average distance detector to improve the response of the average distance detector to the photoelectric effect of the detector. training. - SUMMARY OF THE INVENTION The present invention is an improved method and instrumentation for determining the density of a formation using a series of gamma-ray detectors. This invention can correct the considerable separations found in irregularly shaped sounding wells and, in particular, the larger separations typically found by mandrel-like instruments. In this invention, collimated detectors have varying depths of investigation within the -formation. In small separations, a short-distance detector (DC) mainly investigates the mud and mud scale and a superficial layer of the formation. Unlike the DC detector, a medium distance detector (DM) has a greater depth of investigation and is sensitive to the sounding well and to the formation, even in the case of larger separations. A long-distance detector (.DL) is primarily sensitive to the density of the formation and its reading of the -density is corrected using the separation information of the DM and DC detectors. In addition to measuring the density, this invention can measure the photoelectric factor (FFE) of the -formation. Since the photoelectric absorption preferably eliminates the minimum energy gamma rays, the housing of the instrument must allow the passage of minimum energy gamma rays. This is achieved through the use of a ven - tana composed of a material with low atomic number CZ) or by using a material for the housing of low Z such as titanium. The typical materials of the windows are beryllium and titanium. The housing materials can be titanium or, for low pressure requirements, graphite or high strength carbon composites.