Porosity Logs
Definitions of Porosity and Effective Porosity
The porosity of a formation is defined as the volume of the pore space divided by the volume of the rock containing the pore space. This definition of porosity ignores the question of whether the pores are interconnected or not. Swiss cheese, though quite porous, is of very low permeability since the void spaces are not interconnected. Intergranular porosity is effective porosity. Pores blocked by clay particles, silt, and so
forth, are ineffective. Thus, a preferred definition gives total porosity ( as the volume of the pores divided by the volume of rock, and effective porosity (e) as the volume of the interconnected pores divided by the volume of rock. Figure 1 illustrates this concept.
In a laboratory, porosity can be measured in a number of ways. One
of the simplest is to weigh a sample of rock when it is 100% saturated with water, then remove all the water and reweigh it. Provided the density of the rock matrix (or the volume of the rock sample) is known, the porosity can be found.
On location, the density logging tool provides an in-situ bulk rock density measurement that, if properly rescaled, serves as a porosity trace.
However, measurement of the density of a rock is not the only method available for determining formation porosity. Other methods include neutron and acoustic logging, which we will look at shortly. Whatever logging device is used, we should always remember that porosity devices are sensitive to both rock matrix and to the fluid filling the pore space. Thus, all porosity tool measurements reflect not only porosity, but also the type of rock, the clay content, and the fluid type. No tool has been invented to date that reads just porosity. This limitation of conventional porosity devices is a blessing in disguise, since it allows the analyst to derive more than just porosity from a combination of different porosity tools.
Clean (shale- and clay-free) water-bearing formations of known lithology represent the simplest environments for porosity determination, since the effects of mixed lithology, clay, and hydrocarbons do not confuse the issue. However, before discussing these analysis techniques, let us review the scales used on porosity logs and the procedures and techniques to be used in reading them.
Three things must be determined before reading the log:
- the type of curve recorded, e.g., bulk density, rb, or apparent porosity, rD and, if it is a porosity curve, the lithology used for the porosity calculations
the scale, e.g., 45% to -15% or 60% to 0%, on a neutron log
the actual lithology in the well and the nature of the fluid occupying the pore space
Once all three are determined, true porosity can be found for those intervals where the particular porosity device under consideration can reasonably be expected to work. For instance, with a pad contact device such as the density tool, no readings should be attempted in washed-out zones.
Porosity is the volume fraction of pore space in the rock and is expressed as a fraction of the bulk volume of the rock. The normal convention in reservoir engineering is to express porosities in percentage units; e.g., a porosity of 0.3 is referred to as 30% porosity. However, another term frequently used is "porosity unit," or P.U. Using "unit" rather than percentage avoids a lot of confusion, as, for example, when comparing a 20 P.U. sandstone with a 25 P.U. sandstone. The latter is 5 P.U. higher than the former. This negates the confusion caused by saying one is 5% better than the other or 25% better than the other, depending on which way the difference is expressed.
Frequently a combination of porosity devices is available that can be run into the wellbore together. Such combination tools often can define porosity better than any single device. The most commonly available pair is the density/neutron combination.
When working with well logs generated by such a tool combination, check the log scales carefully before jumping to conclusions. More confusion may exist about density/neutron combinations and their presentations than about any other log on the market today.
Formation Density Tool
Density Log
Density is one of the most important pieces of data in formation evaluation. In the majority of the wells drilled, density is the primary indicator of porosity. In combination with other measurements, it may also be used to indicate lithology and formation fluid type.
A conventional compensated density log is shown in Figure 1 , with the value of formation bulk density (e)in tracks 2 and 3. The most frequently used scales are a range of 2.0 to 3.0 gm/cc or 1.95 to 2.95 gm/cc across two tracks. A correction curve, , is sometimes displayed in track 3 and less frequently in track 2. The gamma ray and caliper curves usually appear in track 1.
The tool can be used by itself or in combination with other tools, such as the compensated neutron tool. The formation density skid device ( Figure 2 ) carries a gamma ray source and two detectors, referred to as the short-spacing and long-spacing detectors. This tool is a pad-type tool; i.e., the skid device must ride against the side of the borehole to measure accurately.
The source continuously emits gamma rays. These pass through the mudcake and enter the formation, where they progressively lose energy until they are either completely absorbed by the rock matrix or they return to one or the other of the two gamma ray detectors in the tool. Dense formations absorb many gamma rays, while low-density formations absorb fewer. Thus, high count rates at the detectors indicate low-density formations, whereas low count rates at the detectors indicate high-density formations.
Gamma rays can react with matter in three distinct manners:
- Photoelectric effect, where a gamma ray collides with an electron, is absorbed, and transfers all of its energy to the electron. In this case, the electron is ejected from the atom.
Compton scattering, where a gamma ray collides with an electron orbiting some nucleus. In this case, the electron is ejected from its orbit and the
incident gamma ray loses energy.
Pair production, where a gamma ray interacts with an atom to produce an electron and positron. These will later recombine to form another gamma ray.
We have already seen that the photoelectric interaction can be monitored to find the lithology-related parameter, Pe. For the conventional density measurement only the Compton scattering of gamma rays is of interest. (Conventional logging sources do not emit gamma rays with sufficient energies to induce pair production.)
Since the density of a mixture of components is a linear function of the densities of its individual constituents, it is a simple matter to calculate the porosity of a porous rock. Consider the bulk volume model of a clean formation with water-filled pore space ( Figure 3 ).
Unit volume of porous rock consists of a fraction made up of water and a fraction (1 -) made up of solid rock matrix.
The bulk density of the sample can be written as:
b + ma (1 +) + f
where ma refers to the matrix density and
f refers to the fluid density. Simple rearrangement of the terms leads to an expression for porosity given by:
D = (ma - b)/(ma - f)
The same concept can be illustrated graphically as in
Figure 4 , where b is plotted against porosity. Note that points falling on the line connecting the matrix point (ma, = 0%) and the water point (f ,= 100%) represent all possible cases extending from zero-porosity rock matrix to 100% porosity. Any intermediate value of b corresponds to some porosity .
The matrix density in normal reservoir rocks varies between 2.87 gm/cc (dolomite) and 2.65 gm/cc (sandstone). The fluid density of normal brines ranges from 1 to 1.1 gm/cc and is controlled by the properties of the invading mud filtrate in permeable zones. Porosity derived from a density log is referred to as D.
The density log gives reliable porosity values, provided the borehole is smooth, the formation is shale-free, and the pore space does not contain gas. In shaly formations and/or gas-bearing zones, it is necessary to refine the interpretative model to make allowances for these additions or substitutions to the rock system.
Introduction
The density of a formation is one of the most important pieces of data in formation evaluation. It is used in the majority of the wells drilled as the primary indicator of porosity. In combination with other measurements, it may also be used to indicate lithology and formation fluid type.
A conventional compensated density log is shown in Figure 5 , with the value of formation bulk density (b)in Tracks II and III. The most frequently used scales are a range of 2.0 to 3.0 gm/cc ore 1.95 to 2.95 gm/cc across two tracks. A correction curve,
sometimes displayed in Track III, is less frequent in Track II. The gamma-ray and caliper curves, if run, are usually plotted in Track I.
The tool can be used by itself or in combination with other tools, such as the compensated neutron tool. Figure 6 illustrates the articulated "skid" device; it carries a gamma ray source and two detectors. This tool is a pad-type tool; i.e., the skid is forced by the tool against the side of the borehole.
Operating Principle
Gamma rays, continuously emitted from the source, pass through the mudcake and enter the formation. Here they progressively lose energy until they are either completely absorbed by the rock matrix or return to one of the two gamma ray detectors in the tool. Dense formations absorb many gamma rays, while low-density formations absorb fewer gamma rays. High count rates at the detectors indicate low-density formations, and vice versa. Fore example, in a thick anhydrite bed the detector count rates are very low, while in a highly washed-out zone of the hole, simulating an extremely low-density formation, the count rate at the detectors is extremely high.
Gamma rays can interact with matter via three distinct mechanisms:
1. Compton scattering: gamma rays collide with electrons orbiting some nucleus. Electrons are ejected from orbit and the incident gamma rays lose energy.
2. Photoelectric effect: gamma rays collide with electrons and lose all energy. Electrons are ejected from the atom.
3. Pair production: gamma rays interact with atoms to produce electrons and positrons; these later recombine to form two 0.511 MeV gamma rays, which depart in opposite directions.
Figure 7 illustrates the concept of the mass absorption coefficient. If an incident beam of gamma rays strikes a target of thickness x, its intensity is reduced on passing through the target in such a way that:
Iout = Iin e-µx
where µ is the mass absorption coefficient. This coefficient µ is a function of both the type of material in the target and the type of interaction that takes place.
Figure 8 shows µ as a function of incident gamma ray energy fore all three types of interaction. The conventional gamma ray source used in logging tools is made of cesium and the emitted gamma rays have an energy of 0.661 MeV. Referring to Figure 8 , it is obviously highly unlikely that any form of pair production will occur, since this type of interaction only occurs at energies higher than 2 ore 3 MeV.
The detectors used in conventional density tools have a practical lower limit to the gamma ray energy level they can detect. This lower limit is about 0.2 MeV. Thus, the operating range, shown on Figure 8 , is between the two vertical lines marking the energy range between the gamma rays emitted from the source and the limit of detection by the detectors. Compton scattering therefore becomes the most probable form of interaction that conventional density tools can monitor.
The net effect of gamma ray Compton scattering and absorption is that the count rate seen at the detector is logarithmically proportional to the formation density ( Figure 9 ):
log (count rate) = A + B • (formation density)
Both near- and far-spacing detectors behave in this way, so that a plot of far versus near count rates also produces a straight line ( Figure 10 ). Note that formation density increases as count rates decrease.
Compensation
A mudcake with a density different from that of the formation changes both the near and far count rates. Figure 11 shows where a plotted point falls if a formation with a bulk density of 2.7 gm/cc has an ever-increasing amount of mudcake of density 1.5 gm/cc placed between it and the tool. In an extreme case of "infinite" mudcake thickness, both detectors "see" only mudcake and read a value of 1.5 gm/cc.
The arc describing the locus of the points is referred to as a rib. The zero mudcake line is referred to as a spine. A complete set of spine and ribs can be drawn fore various thicknesses and densities of mudcakes ( Figure 12 ). Note that ribs also extend to the left of the spine fore mudcakes having a density greater than the formation density; e.g., in barite muds.
The surface equipment associated with the density tool computes the position of the point on the spine and ribs chart, then moves the point along the rib to intercept the spine. At this point, a corrected value of is recorded fore the log. The value of is calculated as the difference between from the long spacing and cor. Thus, is positive in light muds and negative in heavy muds.
Electron Density
Since Compton scattering is an interaction between gamma rays and electrons, the density actually measured is the electron density, e, not the bulk density, b
Since e is not exactly equal to b fore all elements, a special calibration makes the tool read correctly in fresh-water-filled limestone.
As a result of the calibration technique used, not all substances commonly found in rock formations are read correctly by the density tool. Table 1 gives a listing of density properties of various compounds frequently found in subsurface formations.
Density Log Corrections, Quality Control
Density Log Quality Control
Practical calibration of the density tool is accomplished by a series of standards. The primary standard is made by using laboratory formations. Since these cannot be easily transported, a set of secondary standards is available at logging service company bases in the form of aluminum, magnesium, and/ore sulfur blocks of accurately known density and geometry. These blocks, which weigh up to 400 pounds, are not easily transportable either. So a field calibrator containing two small gamma ray sources is used to reproduce the same count rates as those found in the blocks.
The wellsite calibration should be performed before and after each log is run; the shop calibration should be run at least every 60 days, and a copy of it attached to the main log. It is important to note that the field calibrator, the skid with the detectors, and the source form a matched set. If any of the three does not match the serial numbers on the master calibration, the log should be rejected.
Natural benchmarks fore checking the validity of a density log are salt, which has a a of 2.032 gm/cc, and anhydrite, which has a a of 2.977 gm/cc. These minerals may not appear in the wellbore being logged; even if they do, they may not be 100% pure, and should be used with caution. In general, density logs are either well calibrated (and therefore correct) or very noticeably bed.
Apart from the natural benchmarks already discussed, the next best quality check is a review of the curve. If the short-spacing detector fails, then the whole compensation mechanism is thrown out of kilter. So if is roughly within the limits of ± 0.05 gm/cc, the log may be assumed to be correct. If in light muds the is negative, however, something is wrong. Likewise, positive values for in heavy (barite) muds is a danger signal.
Neutron Logs: Introduction
Neutron Log
Neutron porosity devices respond to the hydrogen content of the formation. In clean reservoirs, hydrogen is present in liquid-filled pore space. Neutron logs thus measure the amount of liquid-filled porosity. Neutron logging devices contain a neutron source that continuously emits energetic (fast) neutrons, and one or more detectors. Neutrons collide with formation nuclei, causing them to lose energy. After a sufficient number of collisions, the neutrons reach a lower energy state (epithermal) and continue to lose energy until they reach a still lower energy state (thermal), whereupon they are captured by formation nuclei.
When a nucleus captures a thermal neutron, a gamma ray is emitted to dissipate the excess energy. Porosity (or hydrogen index) can be determined by measuring epithermal or thermal neutron populations or capturing gamma rays or any combination thereof. Neutron logs based on the detection of epithermal neutrons are referred to as sidewall neutron logs. The compensated neutron log, in widespread use today, uses two thermal neutron detectors to reduce borehole effects. Single thermal neutron detector tools, of poorer quality, are available in many areas of the world. Captured gamma rays are used for porosity determination and logs of this type are referred to as neutron-gamma tools. The responses of these devices are dependent upon such variables as porosity, lithology, hole size, hole rugosity, fluid type, and temperature. Compensated and sidewall logs have corrections included in the electronic panels to account for some of these variables, while neutron-gamma logs require corrections from departure curves.
The main applications for neutron tools are three: determination of porosity, formation fluid type, and (in combination with other devices) lithology.
Depending on the device, these applications may be made in either open or cased holes. Figure 1 illustrates a generalized neutron logging tool. Historically, a number of devices have been used that rely on one portion or another of a neutron's progress from a chemical source to eventual capture by formation nuclei.
In addition to porosity, neutron tools respond to other formation parameters and certain borehole environmental effects. Parameters that affect neutron devices include lithology and formation fluid type (e.g., gas). Environmental factors that affect neutron logs include borehole fluid type, density and salinity, borehole size, mudcake, standoff, temperature, and pressure. Modern neutron tools incorporate corrections to some extent for many of these environmental factors, but older (neutron-gamma type) tools do not. Consult service company correction charts for each tool used to assess the magnitude of these effects.
Neutron gamma tools may infrequently be used for cased-hole correlation logging and perforation depth control. Sidewall neutron tools are still available from some service companies, but have mostly been replaced with compensated neutron tools. Compensated neutron tools are widely used and frequently run in combination with compensated density tools. Dual epithermal neutron tools are in the prototype stage and may become more widely available in the future.
Choice of neutron tool should be dictated by well conditions and compatibility with other required services.
Figure 2 shows a schematic of a CNL tool eccentered in a borehole. There are two typical tool string arrangements, one (combined with density and gamma ray) for openhole and one (combined with a collar locator) for cased hole.
Compensated neutron tools are run on a matrix setting chosen by the logging engineer or the company witness. If the actual lithology coincides with the chosen matrix setting, porosities may be read directly from the log. However, this is seldom the case. If the matrix is something other than that used in running the log, the porosity reading from the log will not be correct. Also, in most instances, the lithology is not known prior to logging the well. Therefore, a standard matrix setting is normally used. Figure 3 shows a combination compensated neutron/formation density log.
A convenient standard for the neutron is the neutron porosity index (limestone). This is the same value that the tool would have read had it been recorded on a limestone scale. Figure 4 plots the porosity measured by the neutron tool using a limestone, water-filled matrix against the true porosity for the indicated lines of constant lithology. This chart can be used to determine the true porosity if the actual lithology is known. To obtain the true porosity, enter the measured porosity value on the x-axis, proceed vertically to the appropriate lithology line, then read the true porosity to the left, on the y-axis.
As in the case of density logs, compensated neutron logs may be used as direct indicators of porosity only in clean, liquid-filled, porous formations. The response in shaly or gas-bearing formations calls for special handling.
Introduction
The neutron is a fundamental particle found in the nucleus of all atoms except that of hydrogen, which contains only a proton. Neutrons have approximately the same mass as protons, but carry no electrical charge. Their small size and electrical neutrality make neutrons ideal projectiles for penetrating matter: they pass through brick walls and steel plates with great ease. It is logical that neutrons have found their niche in the logging tool arsenal. Over the years, a number of logging tools have appeared that rely on the neutron's interaction with matter. To fully understand these different tools, let us review certain aspects of nuclear physics.
Two categories of neutron sources are found in the logging industry: chemical sources and pulsed sources. chemical sources are composed of two elements in intimate contact that react together to continuously emit neutrons, usually plutonium/ beryllium ore americium/beryllium. Such sources need to be heavily shielded when not in use.
Pulsed sources incorporate a neutron accelerator and a target, and can be activated by simply switching on the accelerator. These are relatively harmless when not in use. Currently, the pulsed neutron sources are used for pulsed neutron logging and in tools that measure inelastic neutron collisions (carbon/ oxygen-type logs).
Near the chemical sources, "fast" neutrons are found with nearly all their initial energy of several ( ~ 4) MeV. These neutrons interact with the nuclei of other atoms and lose energy with each collision. Eventually, fast neutrons reach an intermediate energy level, where they have an energy of only a few (0.2 to 1.0) eV; in that state they are called epithermal neutrons. After yet more interaction, a neutron may be slowed down to a point at which it has the same energy as the surrounding matter; this energy level is directly dependent on the absolute temperature. Such neutrons are called thermal neutrons, and have energies in the range of 0.025 eV. When a neutron reaches thermal energy it is captured by a nucleus that emits a gamma ray. This gamma ray is called a capture gamma ray.
All conventional neutron logging tools, with the exception of pulsed neutron tools, have operating principles based on the spatial distribution of the neutrons ore the capture gamma rays they produce. Pulsed neutron logs assess distribution as a function of time.
Early neutron tools, known as GNT-type tools, consisted of a chemical source and a single detector of neutron capture gamma rays. This tool, a qualitative indicator of porosity, was badly affected by hole size and the salinity of the borehole fluid and formation water.
In an attempt to cure these inherent problems, the sidewall neutron porosity (SNP) tool was introduced in the early 1960s. It relied on a single detector of epithermal neutrons. This tool overcame general salinity problems, but had its own unique problem in that mudcake could affect its readings, and estimation of the magnitude of the error was not always easy.
The compensated neutron log (CNL) was then introduced in the late 1960s with two detectors of thermal neutrons. It solved most of the defects of the previous tools, yet it, too, encountered problems with formations containing thermal neutron absorbers. The present state-of-the-art is a CNL-type tool with dual detectors of epithermal neutrons that may solve the problem of thermal neutron absorbers. Figure 5 illustrates a generalized neutron logging tool.
The complete solution to the problem of neutron scattering and capture is extremely complex. The ability of a nucleus to slow down ore capture a neutron is measured by its cross section. Cross sections for slowing down or capturing neutrons vary with different elements and with neutron energy.
Two elements, hydrogen and chlorine, dominate the behavior of all neutron tools. Hydrogen, being the element with a single proton fore a nucleus, provides the best material for slowing down a neutron. Simple mechanics reveals that when two balls collide, the maximum energy loss occurs when the two balls are of equal mass. Thus, the equal mass of hydrogen's neutron and proton account for its prodigious power to slow down neutrons.
Chlorine has a large capture cross section for thermal neutrons, absorbing them a hundred times faster than most other elements. After accounting for the relative abundance of all the elements and their slowing down cross sections and capture cross sections, it transpires that a neutron need collide with a hydrogen nucleus an average of 18 times to reach thermal energy. Once a neutron does reach thermal energy, it is very likely to be absorbed by a chlorine nucleus.
This explains why the original GNT tools had such a dependence on fluid salinity. A few parts per million of sodium chloride in the mud ore the formation water could alter their response dramatically. It also explains why the SNP was such an improvement over GNT. The tool was completely blind to capture gamma rays, since it only detected epithermal neutrons. The CNL tools theoretically are just as blind to salinity effects, since they, too, ignore the capture gamma rays from chlorine. But small additions of boron or cadmium in the formation can seriously affect the distribution of thermal neutrons.
Compensated Neutron Tool
The Compensated Neutron Tool (CM)
The compensated neutron tool measures a neutron porosity index which relates to the porosity of the formation only if the lithology and formation fluid content are known. Conventional stacking arrangements are shown in Figure 1 . The tool consists of a chemical neutron source and two detectors of thermal neutrons ( Figure 2 ). It is run eccentered with the source, with detectors forced against the borehole wall by means of a bow spring.
Conventional compensated neutron tools can be run equally well in open ore cased, liquid-filled holes. In an empty hole (gasfilled), they do not work and epithermal neutron tools are required. It is normal practice to run these tools in combination with the density and gamma ray tools.
CNL operating Principle
To properly understand the operation of the CNL logging tool, the distribution of thermal neutrons moving away from the source must be investigated. The thermal neutron flux is defined as the number of thermal neutrons crossing unit area in unit time. This flux is controlled by the hydrogen content of the formation. Hydrogen is found in the water molecules filling the pore space (assuming the formation to be water bearing). Thus the hydrogen content of the formation is a direct indication of its porosity.
Figure 3 shows a plot for three different values of porosity of the thermal neutron flux as a function of the distance from the source. Note that the lines intersect at some distance from the source. At points closer to the source than the intersection, high thermal neutron flux means high porosity, but at points farther from the source, high thermal neutron flux indicates low porosity.
The absolute count rate is a poor indication of porosity: too many factors affect it. The actual count rate seen at any detector spacing from the source is a function not only of porosity, but also of such environmental factors as hole size, mud weight, and casing size and weight. Therefore, the CNL reading must be normalized to correct fore unknown environmental effects. This is done by taking two readings of thermal neutron flux at different spacings and using them to define the slope of the response line. This slope is relatively unaltered by environmental effects, although the position of the response line on the graph may vary in the "y" direction substantially. Figure 4 illustrates this concept.
The primary measurement of the CNL tool is thus a ratio of two count rates. A high ratio indicates high porosity. The conversion of the ratio to a porosity value is based on laboratory experiments conducted with rock samples of known porosity. Figure 5 shows the results of such experiments.
To record porosity directly, a technique must be developed to convert the ratio into porosity. Fore example, a ratio of 2.0 could mean less than 10% porosity in dolomite or more than 20% in sandstone. The surface controls of the CNL tool allow the operator to select the matrix for which a porosity is required. Thus, if the operator chooses to run the CNL on a limestone setting, the conversion of ratio to porosity follows the middle of the three response lines. If, subsequently, the operator finds that the actual matrix is not limestone, then it is necessary to convert the apparent limestone porosity to some other matrix porosity. Correction charts, such as the one shown in Figure 6 , make this an easy task. This chart shows that the relationship between apparent limestone porosity and the porosity values for dolomite and sandstone is fairly uniform, with the exception of the very high and the very low porosity values. In midrange apparent limestone porosity values, certain approximate rules of thumb can be used.
Environmental Corrections
Corrections fore environmental factors are generally small and can be estimated from wireline service company charts. Of all corrections, the temperature and borehole size corrections are the largest.
Depth of Investigation
The depth of investigation of the CNL depends on both the formation porosity and the salinity of the mud filtrate (invading water) and formation water. It can be expressed in terms of a geometric factor, J:
CNL = J (CNL) Invaded + (1 - J) (CNL)Uninvaded
J is a function of the depth of invasion measured from the borehole wall. Figure 7 shows a typical set of J curves fore the MSFL, the density, and the neutron tools. Other J curves apply fore a different salinity mud filtrate. In Figure 7 we see that none of the three tools can penetrate very deeply into the formation, but that the CNL has the greatest depth of investigation. It obtains 90% of its response from the first 10 in. of formation, compared to 6 in. for the FDC tool. Finally, depth of penetration is also a function of the porosity and the formation fluid.
Matrix Settings and Lithology Pore and Fluid Effects
when choosing a neutron logging scale and matrix setting, it is good practice to remain consistent with the standard operating procedure fore the particular lithology expected in the well.
Sand/Shale Sequences The log should be run with a sandstone matrix setting and with a porosity scale of 60% to 0% left to right across Tracks II and III. If a density log is also recorded, then it should be scaled as an apparent sandstone porosity on the same scale ( Figure 8 ).
Carbonates/Evaporites/Generally Unknown Lithology The log should be run on a limestone matrix setting with a porosity scale of 45% to -15% left to right across Tracks II and III. If a density log is also recorded, then a scale of 1.95 to 2.95 gm/cc is required. An example is shown in Figure 9 .
The advantages of the compatible sandstone scales are that (1) gas can be easily spotted (neutron reads less than density) and (2) shales can be distinguished from sands (neutron reads more than density).
The advantage of the compatible limestone scales is that both curves coincide in limestone, and the neutron reads less than the density in sands and more than the density in dolomite and shales.
Gas Effects
Liquid hydrocarbons have hydrogen indexes close to that of water. Gas, however, usually has a considerably lower hydrogen concentration which varies with temperature and pressure. When gas is present near enough to the borehole to be within the tool's zone of investigation, a neutron log reads too low a porosity. This characteristic allows the neutron log to be used with other porosity logs to detect gas zones and identify gas-liquid contacts.
In a manner entirely analogous to the approach taken with the density tool, the neutron tool response in gas-bearing formations may be written as
N = Nma (1 - ) + Nmf
Sxo + Nhy (1 - Sxo)
where:
Nma is the response to matrix (usually considered equal to zero),
Nmf is the response to mud filtrate (usually considered equal to 1), and
Nhy is the response to hydrocarbon
Rearrangement of the terms gives
= (N - Nma) / (Nhy - Nma + Sxo (Nmf - Nhy))
If it is assumed that Nma and
Nhy are very small and Nmf is equal to 1, then
= N / Sxo
Since Sxo is always less than 1, it follows that N in hydrocarbon-bearing formations is always less than .
Shale Effects
In general, response of the neutron may be written in the form
N = T + Vsh
Nsh
where:
N is the log reading
T is the true porosity
Vsh is the bulk volume of shale, and
Nsh
is the response of the neutron tool in pure shale.
Typical values of Nsh for compensated neutron tools lie between 20% and 45%. The value of Vsh can be estimated from the gamma ray, SP, or neutron/density combinations. A corrected porosity may thus be found using
T = N - Vsh
Nsh
CNL Calibration and Quality Control
The compensated neutron tools are calibrated in a large water-filled tank. This shop calibration is carried out at 60-day intervals. Practical quality control can be monitored by the usual criteria for all curves plus two natural benchmarks, which are salt (NML = -0.3%) and anhydrite NML= 0.2%). Apparent neutron and density porosities should agree in clean, water-bearing zones where lithology is known.
Accoustic Measurement:: Introduction
UNDER CONSTRUCTION … !
Accoustic Logging Tools
Acoustic Log
Acoustic tools measure the speed of elastic waves in subsurface formations. These measurements are used to calculate, measure, detect and/or estimate porosity, lithology, integrated travel time, true time scales, fractures, synthetic seismogram, the bond between casing, cement, formation, and formation overpressure.
A typical acoustic log is illustrated in Figure 1 . Curves recorded on acoustic logs may include the interval transit time, , in microseconds/ft (the reciprocal of speed), caliper, gamma ray and/or SP, and integrated travel time.
Tools currently available for making this measurement include the borehole-compensated tool, a slim tool version that can be run through tubing; and the long-spacing sonic tool.
These tools include transmitter transducers that convert electrical energy into mechanical energy and receiver transducers that do the reverse. In its simplest form, the measurement is made in an uncompensated mode ( Figure 2 ). The transmitter emits a small acoustic wave at time 0 that travels through the mud to the borehole wall, where it is refracted through the formation. Part of the energy traveling through the formation in turn is refracted back into the mud column and finds its way to the first receiver at time T1, and to the second receiver at time T2. The difference in the two times is referred to as and represents the time a compressional wave takes to travel through the formation a distance equal to the spacing between the two receivers. If this distance is one ft, then the formation travel time, , is expressed in microseconds/ft.
This early form of sonic tool relied on the fact that the travel paths to the two receivers were equal in the mud. This was true in the case of a smooth borehole of unchanging size, but was not true if the borehole was of varying size or if the sonde tilted with respect to the axis of the borehole.
These difficulties were overcome by the introduction of the borehole-compensated sonic tool. Figure 3 illustrates the principle of the compensated sonic tool.
Multiple transmitters and receivers are employed and two values of are measured and averaged. The net result of this system is the elimination of errors in due to sonde tilt and hole size variation. Even so, there are practical limits to the working range of the tool (e.g., in large holes).
The long-spacing sonic tool was introduced in an attempt to overcome borehole environmental problems. For example, when a shale formation is drilled, the shales exposed to the mud frequently change their properties by absorption of water from the drilling mud. The travel time for elastic waves therefore changes too. In order to read the travel time in the undisturbed formation further from the borehole, a longer transmitter-receiver spacing is required. Typically, a long-spacing sonic tool has a transmitter-receiver spacing of 8, 10, or 12 ft.
Lengthening the spacing on a sonic device achieves two ends:
A more valid acoustic log may be recorded in a bigger hole with a long-spacing device than with a conventionally spaced tool.
The zone investigated by the tool is deeper into the formation with a long-spacing device than with a conventionally spaced tool.
The long-spacing tools make their measurements in a "depth-derived" mode; i.e., the borehole compensation is actually achieved by memorizing travel times measured when the tool is at one depth and combining those with travel times recorded at a shallower depth when an alternate combination of transmitters and receivers is activated.
The fact that compressional waves travel faster through solid matrix material than through fluid is the basis for the method used to determine formation porosity from sonic logs. Figure 4 gives a schematic in which the pore space and the solid matrix have been separated for the purposes of illustration. If f is the time taken to travel through the pore space and ma is the time taken to travel through the matrix, the total travel time measured will be , and the porosity will be given by
total travel time measured will be , and the porosity will be given by
= + (1 ) ma
or
This is known as the Wyllie time average equation. Note that it is not an exact solution for porosity, but an approximation.
Matrix travel time depends on the matrix itself. Table 1 gives a partial listing of common matrix materials and fluids.
Fluid travel time is a function of the temperature, pressure, and salinity of a solution. A commonly used default value for
f is 189 µsec/ft.
Unconsolidated formations exhibit longer travel times than can be accounted for by the Wyllie time average equation. This discrepancy can be handled in two ways: conventionally, and by the Hunt transform. The conventional method merely adapts the Wyllie time average equation by introducing the factor Bcp, such that
where Bcp is some number greater than 1. This can be done by estimating Bcp from the transit time in shales adjacent to the formation of interest. Then
Bcp - shale/l00
Thus, if, in a shallow sand-shale sequence, log shale is 130 µsec/ft, then a Bcp of 130/100, or 1.3, should be used. The Hunt transform is based on empirical observations from sonic logs and porosity determinations from other means. Figure 5 shows the generalized form of the Hunt-Raymer transform compared to the Wyllie formula, and plots against porosity for sandstone, limestone, and dolomite. An acceptable equation relating porosity to for this transform is given by:
Note that fluid does not appear as a term in this equation. The assumption is that the fluid is liquid (not gas) and is built into the coefficient 1/( - ). In sandstones this coefficient is very close to 5/8.
Compaction effects manifest themselves on sonic logs as a decrease of with depth. This is particularly evident in shales. The deeper a shale is buried the more compact it becomes and the shorter the . In cases where there is no escape for the water in the shale, compaction ceases and over-pressure results. The shale at that depth is so anomalously high that it becomes an indicator of formation pressure. Obtaining readings on a sonic log in shales only and plotting these sh values against depth yields a "normal" gradient. Departures from this gradient indicate overpressure.
To summarize, porosity, in clean formations of known lithology, may be determined from all three common "porosity" tools. Complex cases, where mixed lithology, clays, and light hydrocarbons coexist, call for a more sophisticated approach.
Acoustic Logging Tools
Acoustic logging tools measure the formation properties tc and ts by the use of apparatus suspended in the mud column. Borehole compensation, long-spacing tools, and waveform recording may assist in this task.
A typical acoustic log is illustrated in Figure 6 . Curves recorded on this log are the interval transit time, t , in microseconds/ft (the reciprocal of speed), caliper, gamma ray and/or SP, and integrated travel time.
Tools available to make the measurement include borehole-compensated (BHC) tools, slimmer tool versions that can be run through tubing, and long-spacing acoustic tools. In seismic data gathering, a disturbance is made at the surface by explosives, for example, ore by use of an air gun in water. In acoustic logging, an acoustic pulse--produced by alternate expansions and contractions of a transducer--is emitted by a transmitter. A typical pulse of this sort is shown in Figure 7 .
This transmitter pulse generates a compressional wave through the mud. Part of the acoustic energy traverses the mud, impinges on the borehole wall at the critical angle of incidence, passes along the formation close to the borehole wall, reenters the mud, and arrives at a receiver, where it is converted into an electrical signal ( Figure 8 ).
Operating Principle
In its simplest form, measurement is ma e in an uncompensated mode ( Figure 9 ). The transmitter emits compressional wave at time 0 that travels through the mud to the borehole wall, where it is refracted through the formation. Part of the energy traveling through the formation, in turn, is refracted back into the mud column and finds its way to the first receiver at time T, and to the second receiver at time T2. The difference in the two times is referred to as t and represents the time taken for a compressional wave to travel through the formation a distance equal to the spacing between the two receivers.
This early form of acoustic tool relied on the fact that the travel paths to the two receivers were equal in the mud. This was true in the case of a smooth borehole of unchanging size, but was not true if the borehole was of varying size ore if the sonde tilted with respect to the axis of the borehole. These difficulties were partially overcome by the introduction of the BHC (borehole-compensated) acoustic tool. Figure 10 illustrates the principle of the BHC acoustic tool.
Schlumberger uses two transmitters and four receivers, and two values of t are measured and averaged. The net result of this system is the reduction of errors in t that are caused by sonde tilt and hole size variation. Even so, there are practical limits to the working range of the tool (e.g., hole size). In large boreholes, the time taken fore a compressional wave to travel from the transmitter to the formation, through the formation, and back through the mud to a receiver may exceed the time taken fore a direct transmission from the transmitter to the receiver through the mud. The critical factors in determining when this condition exists are the transmitter-receiver spacing, the hole size, and the travel time in the formation. With conventional borehole-compensated acoustic tools with a 3-ft spacing, the highest t formation that can be measured is 175 µs/ft in a 12-1/4 in. hole and 165 µs/ft in a 14-in. hole. This limitation is not serious if the formation is a reservoir rock with a t in the normal range of 40 to 140 µs/ft. It does become a serious defect if the rock is a shale of long transit time and the purpose of the log is to compute integrated travel time fore geophysical purposes.
Long-Spacing Acoustic Tool
The long-spacing acoustic tool was introduced in an attempt to overcome environmental problems. When a shale formation is drilled, the shales exposed to the mud frequently change their properties by absorption of water from the drilling mud, so the travel time for elastic waves changes, too. In order to read the travel time in the undisturbed formation away from the borehole, a longer transmitter-receiver spacing is required. Typically, a long-spacing acoustic tool will have transmitter-receiver spacings of 8, 10, or 12 ft. Figure 11 shows a comparison of a conventional borehole-compensated acoustic log with a long-spacing acoustic log.
Lengthening the spacing on a acoustic device achieves two ends:
A valid acoustic log may be recorded in a bigger hole with a long-spacing device than with a conventionally spaced tool.
The zone investigated by the tool is deeper into the formation with a long-spacing device than with a conventionally spaced tool.
Deeper investigation into the formation is of great value when logging through intervals of shale that have had their properties altered by the drilling process. Provided t of the formation in the undisturbed state is less than t of the formation in the altered state, the quickest route for a compressional wave is via the undisturbed formation, or "deep" in the formation. Figure 12 illustrates this effect.
The long-spacing tools make their measurements in a "depth-derived" mode; i.e., the borehole compensation is actually achieved by memorizing travel times measured when the tool is at one depth and combining those with travel times recorded at a shallower depth when an alternate combination of transmitters and receivers is activated. (The long-spaced sonde would be too long if used in the same configuration as the BHC tool.) Two transmitters spaced 2 ft apart are located 8 ft below a pair of receivers that are also 2 ft apart ( Figure 13 ).
Memorizing the first t reading and combining it with a second t reading (measured after the sonde has been pulled the appropriate distance farther along the borehole) compensates for the hole size changes.
Cycle Skipping and Noise
The actual travel time measurement is determined at the first arrival peak. However, the tool's internal trigger mechanism for detecting this peak is subject to some errors. Figure 14 illustrates two common problems. In the first, the bias level is set too high and the travel time is triggered by a later peak, causing an erroneously long time to be measured (this is known as cycle skipping). In the second, the bias is set too low and the travel time is triggered by noise, causing an erroneously short travel time.
In the BHC mode, it is not always possible to distinguish between cycle skipping and noise, since two measurements are effectively averaged by the tool.
Log Quality Control
Acoustic logs are subject to very easily detected errors, such as cycle skips and noise. More subtle errors can be pinned down if the log is run through such marker beds as a salt (t=67 µsec/ft) anhydrite (t= 50 µsec/ft) ore into the casing. In the casing, it should read 56 µsec/ft, the travel time in steel, provided the casing is not bonded to a formation of high interval velocity such as a tight limestone.
Accoustic Measurement: - Special Application
Waveform Recording
Waveforms may be recorded fore processing using the long-spaced acoustic tool. The longer spacing allows a larger time separation fore the compressional and shear wave arrivals.
The various transmitter-receiver combinations permit four waveforms to be recorded at 6-in. intervals. Figure 1 illustrates composite waveforms received at the near and fare receivers when the upper transmitter is fired.
Digitization of the waveforms is normally made at a 5 sec sample interval for 512 samples, i.e., 2560 microseconds. A delay of 200 to 500 microseconds is an input parameter selected by the logging engineer.
Waveform recording considerably extends the range of applications of acoustic logging both in open holes and cased holes. The principal benefit is determination of the shear wave velocity of the formation.
The objective of waveform processing is to distinguish between the compressional and shear wave arrivals and to measure their interval transit times. Furthermore, in cased holes formation arrivals are usually distinct from casing arrivals, thereby permitting a viable acoustic measurement where previous acoustic devices would have been ineffective.
Data-processing methods used to extract shear wave arrival times are somewhat complex, and mirror seismic-processing methods; i.e., multiple waveforms are "stacked." Yet it is quite common to "see" shear arrivals on variable density displays of the sort shown in Figure 2 .
Vertical Seismic Profile (VSP)
Another seismic application related to the acoustic log is the vertical seismic profile (VSP). By suspending a geophone in the wellbore and actuating an energy source at surface, reflections of compressional waves may be recorded. Some of these arrive at the geophone after being reflected from beds below the bottom of the well. Thus the VSP affords a method of looking ahead of the drill bit. A schematic of the setup to make a VSP survey is shown in Figure 3 , and an example of the results in Figure 4 .
Exercise 1.
In a dolomite formation in which
ma = 2.87
b = 2.44
f = 1.0 (fresh water)
Find D.
Solution 1:
The equation we use is
Rearranging to solve for
or
(to get rid of negatives)
Substituting values for ma
f and
The solution is
Exercise 2.
In a sandstone formation in which
ma = 2.65
b = 2.40
f = 1.1 (salt mud filtrate)
Find D.
Solution 2:
Using the equation computed in the previous exercise,
=0.16
The solution is
Exercise 3.
In a gas-bearing sandstone, at 10,000 ft the density log reads 1.99 gm/cc or 40% apparent sandstone porosity. Estimate the true porosity, given that Rmf at formation temperature is 0.2 ohm-m and Rxo is 20 ohm-m. Assume mf
is 1.0 gm/cc.
Solution 3:
ma | = 2.65 |
b | = 1.99 |
Rmf | = 0.2 |
Rxo | = 20 |
depth | = 10,000 |
mf | = 1.0 |
Volumetrically, the tool response is as follows:
B = ma (1 - ) + mf (Sxo) + g(1 - Sxo)
According to Archie,
A simple F, relation is
So,
g can be approximated by
g | = 0.l8/[(7644/depth) + 0.22] |
| = 0.18/[(7644/10,000) + 0.22] |
| = 0.18/(76 + 0.22) |
| = 0.18/0.98 |
| = 0.184 |
Then,
g cor | = 1.325 g - 0.188 |
| = 0.243 - 0.188 |
| = 0.055 |
So,
b | = ma(1 ) + mf(Sxo) + Sxo)g(1 |
| = ma ma + mf(Sxo) + g |
Substituting
for Sxo
and substituting in values,
1.99 = 2.65 - 2.65 = 1(0.1) + 0.055 - 0.055(0.1)
1.99 = 2.65 - 2.65 + (0.1) + 0.055 - 0.0055
2.65 = 2.65 - 1.99 + 0.1 + 0.055 - 0.0055
2.65 = 0.810
=
= 0.306
The solution is = 30.6%.
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