CRAIN'S
PETROPHYSICAL
HANDBOOK
c. 1978 - 2008 E. R. (Ross) Crain, P.Eng.
Rocky Mountain House, Alberta Canada T4T 2A2
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Updated 05 Aug 2006
CHAPTER NINETEEN: LOGGING TOOL THEORY Table
of Contents Publication History: Sections 19.08 was published in CWLS InSite magazine Spring 2004. Section 19.10 and 19.11 are repeats of material in Chapter Eighteen. The balance was condensed from various service company publications Aug 2006. Additional material inserted Apr 2007. 19.00 Introduction 19.01 What Is Well Logging? In its most usual form, an oil well log is a record displayed on a graph with the measured physical property of the rock on one axis and depth (distance from the surface) on the other axis. More than one property may be displayed on the same graph. None of the logs actually measure the physical properties that are of most interest to us, such as how much oil or gas is in the ground, or how much is being produced. Such important knowledge can only be derived, from the measured properties listed above (and others), using a number of assumptions which, if true, will give reasonable estimates of hydrocarbon reserves. The use of well logs for evaluating mineral deposits other than oil and gas, such as coal, potash, uranium, and hard rock sequences has been practiced since the early 1930’s and is widespread today. Although the vast majority of logs are run to evaluate oil and gas wells, an increased number are being run yearly for other purposes, including evaluation of geothermal energy and ground water. A large portion of this handbook is aimed at oil and gas, but the other topics are not ignored. Most Chapters apply to both hydrocarbon and mineral exploration. When logs are used for purposes other than evaluation of oil and gas, they are often called geophysical logs instead of well logs. The science is called borehole geophysics instead of petrophysics. This difference is merely a matter of semantics and training. The theory doesn't change - just the nomenclature, and sometimes the emphasis.
19.02 Creating the Well Log
A logging tool is made up of a sonde and a cartridge. The sonde is the portion of the tool which gives off energy, receives energy, or both. The cartridge contains the electrical circuitry or computer components needed to control the downhole equipment, and to transmit data to and from the surface. Combination logging tools consist of more than one sonde and cartridge, so that more than one log can be recorded on a single trip into the wellbore. Surface equipment is mounted in a logging truck, van, or skid unit from which all logging operations are controlled. The logging unit contains hoisting equipment for lowering and raising the tools in the hole, and electronic or computer equipment for controlling and recording the downhole measurements. Measurements are recorded in two forms, analog and digital. The analog data may be recorded on photographic film, electronic plotter, or chart recorder. The same data are captured in digital form on magnetic tape or disc for later use in computer aided analysis. Many instrument control and calibration functions are now handled by the same computer used to record the digital data, with some human control. The result is a log, as seen below. All logging tools and surface equipment must be properly calibrated. Service companies have calibration procedures for most tools, some of which are based on standards established by the American Petroleum Institute (API). Each tool must be calibrated at the surface before placing it in the hole to make measurements, and must pass certain calibrations after the measurements are complete to verify that measurement accuracy has not drifted. Some tools also have downhole calibration checks. After reaching total depth, or some other location of interest in the borehole, measurements are made while pulling the tool upward over several hundred feet of the borehole. This is called the repeat run, and is used to determine the repeatability of the measurements when compared to the main logging pass. After the repeat run is complete, the tool is lowered to the bottom of the hole, and the main logging pass is commenced. During the early portion of these measurements, the responses are compared to those of the repeat run to determine that no instrument drift has occurred. Results of all field calibrations and repeats are attached to the bottom of the well log record. In addition to the actual measurements, the well log itself contains information about the logging process which supports use and interpretation of the data. The well name, location, date, surface measurements on the mud system, drill bit size, casing information, and logging equipment data are found on the log heading, Any pertinent information or comments regarding the logging job may be recorded in the remarks section. The logging equipment is carried to the wellsite on a truck (for land based operations near roads), or transported by helicopter on skids (for remote land operations) or are permanently mounted on offshore rigs. Some typical logging units are shown below. Computerized surface equipment is now the rule rather than the exception. Such units, on a truck and with logging tools on board, can cost over $1,000,000. 19.03
TOOL THEORY – ELECTRICAL SURVEY WHERE: The unit of resistance is the Ohm, named after Georg Ohm, an early pioneer in the electrical field. Resistivity is the resistance of a unit volume of a material. In the metric system, the unit of length is the meter, and area is the square meter. Thus, resistivity is measured in units of ohm - meters squared per meter (ohm-m2/m), often abbreviated as ohm-m. Resistivity also equals the ratio of voltage to current, if the length and area are equal to unity. Thus: WHERE: Conductance is the inverse of resistance: WHERE: Units of conductance are measured in Siemens, also named after an early electrical pioneer. The previous name of the unit of conductance was mho, the reverse spelling of ohm. Conductivity is the inverse of resistivity: WHERE: The units of conductivity are Siemens-meters per square meter, or Siemens/meter (abbreviated S/m). The old name was mho/meter.
In well logging, conductivity is usually given in milli-mho/m or milli-Siemens/m.
Thus in well logging usage: WHERE: Milli-mhos should not be confused with Milli-Ways, a reasonably good restaurant at the end of the Universe. The Electrical Survey, also known as the ES Log, measures resistivity with direct current (DC) using the principles of Ohm’s Law. The basic measuring system has two current electrodes, A and B, and two voltage measuring electrodes, M and N. A current is passed between A and B, and the resulting voltage is measured at M and N as in Figures 5 and 6. If the formation is uniform, the formation resistivity, Rt, can be computed from the formula Rt = K * V / I, where V is the voltage between M and N, and I the intensity of the current flowing from A to B. K is a geometric factor that depends upon the relative distance between A, B, M, and N and is a constant for a given electrode arrangement. In practice, the formula gives a weighted average resistivity of the formation, including a small portion of the borehole. This average is known as the apparent resistivity, Ra. Borehole environment correction charts, available from service company chartbooks, are used to correct Ra to approximate Rt. Modern computer software is available to convert Ra to Rt using sophisticated resistivity inversion mathematics, based on an earth model based on a short spacing resistivity curve. Two types of electrode arrangements are used, the Normal device, and the Lateral device. The electrode arrangement and basic circuitry of the Normal device are illustrated in Figure 19.05. Electrodes A and M are on an insulating mandrel, called the probe or sonde or logging tool, which is suspended at the end of the logging cable. Electrodes B and N are placed far from A and M, and are either at the surface of the ground or on the cable at a long distance from A and M. The distance AM is known as the spacing. The depth reference point of the measurement is the midpoint between A and M. The usual electric log has two Normal devices with spacings of 16 inches (short Normal) and 64 inches (long Normal). The depth of investigation is in the order of the spacing. For the actual Lateral device, current electrodes A and B are placed on the probe. Voltage electrode M is above the current electrodes, generally on the cable, as in Figure 19.6. Note that the AB and MN electrodes can be interchanged, with no change in the measured result (the lw of reciprocity). Electrode N is at the surface of the ground or on the cable at a large distance above A. The midpoint between A and B is the depth reference point, O. The distance MO, usually referred to as AO on log headings (in honour of the original tool design), is defined as the spacing: it is always several times longer than the span AB. With the usual electric log, the spacing is 18 feet 8 inches, and the span is 32 inches.
The shape and dimensions of the volume sampled by a Lateral device depend upon the resistivity distribution around the probe. In soft formations, the bulk of this volume is contained in a cylinder with height AB and radius approximately the spacing MO (or AO). The radial depth of investigation is about 19 feet, and the measurement gives the average resistivity of an interval 32 inches thick. The Lateral curve has strange curve-shape artifacts that reduce its usefulness in formations less than 20 feet thick (Figure 19.7). Complicated interpretation rules are required for thinner beds. Modern resistivity log inversion software is available, using the 16” Normal for bed thickness control, so that Rt can be calculated from the Lateral curve. In practice, the Lateral curve, two
Normal curves and the Spontaneous Potential are recorded, using
a mechanical switch, called a pulsator, to sequentially make
the four measurements using only six electrodes (and six wires
to the surface).
Electrical Survey (ES) Curve Names
Halliburton and Welex Note: Halliburton inverse lateral is same electrode configuration as Schlumberger lateral (blind spot at bottom of zone). Lateral and normal spacings could vary. Point resistivity is uncalibrated (even though a scale is shown) and cannot be used quantitatively.
19.04
TOOL THEORY – SPONTANEOUS
POTENTIAL This is a passive measurement. That is, no energy is provided by the logging tool. There is no SP until the borehole is drilled and filled with conductive muds. This contrasts with telluric currents caused by solar radiation and Northern Lights, and man-made currents from power lines, cathodic protection of pipelines, and welding equipment grounded to the rig while logging proceeds. All these currents can persist without a borehole, but more importantly, can cause anomalies on the SP log, and in some cases rendering it useless. The SP is the result of several electromotive forces: shale membrane potential Em, liquid-junction potential Ej, and electro-kinetic potential Ek. Shales are permeable to sodium ions (Na+) but impervious to chloride ions (Cl-). When a shale separates two sodium chloride solutions of different concentration (the mud in the borehole and the water in the formation), sodium ions migrate by diffusion from the higher concentration into the lower concentration. This movement of positive charges builds up a voltage known as shale potential or membrane potential Em. When two sodium chloride solutions of different concentration are separated by a semi-permeable partition that permits the passage of ions from one side to the other, but prevents bulk mixing of the two solutions, ions migrate by diffusion from the concentrated solution to the dilute solution. This happens at the boundary between the invaded and un-invaded zones. The negative chloride ions have a greater mobility than the positive sodium ions. There is a net transfer of negative electric charges from the more concentrated solution to the less concentrated. The resulting electromotive force is known as the liquid-junction potential Ej. The current loops in Figure 19.08 circulate between shale, borehole, invaded zone, and un-invaded zone and back to the shale. They represent the sum of membrane and liquid junction potentials, which is known as the electrochemical component of the SP. The curve to the left of Figure 19.08 is the corresponding SP curve as measured by a real tool. The square static SP is the theoretical shape of a perfect SP curve. The numerical values of the electromotive forces depend on the type and quantity of dissolved salts. The electrochemical component of the SP is defined mathematically by Ec = Em + Ej = –K * log(Aw / Amf). Aw and Amf are the chemical activities of the formation water and mud filtrate, respectively. K is a factor that depends on the temperature. For clean sands and sodium chloride solutions, K ranges from 67 millivolts at 50 F to 123 millivolts at 300 F. K is reduced when the permeable beds contain dispersed shale.
The chemical activity of a solution is proportional to the salt concentration which, in turn, is inversely proportional to the fluid resistivity. Therefore, the formula becomes Ec = –K * log(Rmf/Rw). Rw and Rmf are the resistivity of formation water and mud filtrate. The above equation needs a bit of help when the two solutions contain salts other than pure NaCl. The passage of an electrolyte through
a porous medium also produces an electromotive force, called
electro-kinetic potential, Ek, between any two points along
the electrolyte flow path. For example, an electro-kinetic
potential is developed when mud filtrate passes through a mud
cake into the formation. The value of this potential is small
and is commonly disregarded in electrical logging. The 64” normal, with or without borehole corrections, is often taken as a measure of deep resistivity RESD (or Rt). Resistive beds are thinner on logs than the true thickness, by a distance equal to the tool spacing (16 or 64 inches for normal resistivity curves).
19.05
TOOL THEORY – INDUCTION
LOGS
1. alternating
current applied to transmitter coils The basic equations for a single transmitter – receiver coil pair, in EXTREMELY simplified form, are shown below.
1: Bt = uo * dI/dt
magnetic field due to current “I” in transmitter coil
Where; I = current circulating in the rock C = conductivity of rock
dBt/dt
= rate of change of transmitted magnetic field The magnetic fields, and currents in the formation and receiver-transmitter system are vectors (amplitude and direction). The in-phase component measured at the receiver coil is called the Real (or R) component. The signal that is 90 degrees out of phase is called the Imaginary (or X) component. Older tools could measure only the R component. Newer tools measure both R and X components. The X component is used to enhance bed resolution by use of proprietory algorithms. If you can handle advanced calculus and know what the “curl” operator does, refer to “Basic Theory of Induction Logging” by J. H. Moran and K. S. Kunz, SEG Oct 1959 for the real story on induction log theory.
The eddy currents induced in a conductive formation experience phase shift and attenuation. The loss due to attenuation is known as skin effect (or propagation loss) and is corrected by proprietary service company algorithms. Figure 19.10A represents a two-coil induction logging system consisting of a single transmitter and receiver surrounded by a loop of homogeneous rock. The voltage at the receiver from a unit loop of radius, r, and altitude, z, with respect to the center of the coil system is given by: Vr = K * G * COND, where K is a function of the area of the transmitter and receiver coils, distance between the coils, current in the transmitter, and frequency of the transmitter current. G is the geometric factor, which depends on the geometric position of the unit loop as related to the transmitter and receiver coils. The radial geometric factor G considers the formation as the combination of a large number of cylinders coaxial with the borehole. The integrated radial geometric factor, Gr, is the sum of all the G values for the total volume within a cylinder of radius, r. This represents a thick homogeneous formation invaded by mud filtrate where conductivity changes radially, and includes a small portion of the borehole. The signal measured by an Induction log positioned opposite a thick formation usually reflects the conductivity of that formation; however, in thin formations, the signal is affected by the conductivities of the adjacent formations. In a similar manner, the integrated vertical geometric factor, Gv, becomes the sum of the G values for all of the volume above (or below) a horizontal plane at a distance, z, from the center of the coil span. The integrated vertical geometric factor increases with the vertical distance, z, and must equal unity for all space. Development of the geometric factor for a focused induction log can be accomplished by adding algebraically all combinations of transmitter-receiver coil geometric factors times each coil pair's contribution to the total instrument response. This is done by computer modeling at the time the tool is designed. To illustrate the geometric factor
concept, assume borehole size = 8 in, invasion diameter = 40
in, Cm = 1000 mmho/m, Ci = 50 mmho/m, Cu = 100 mmho/m. For
a particular induction log, assume Gm = G8 = –0.001,
Gi = G40 – G8 = 0.025 – (–0.001)
= 0.026, and Gu = 1 - G40 = 1 – 0.025 = 0.975. CONDa
= Gm * Cm + Gi * Ci + Gu * Cu The borehole and invasion create a 2.2 mmho/m error (100 – 97.8) in the measured value of the un-invaded zone conductivity. Bed thickness correction charts are provided by service companies for their particular tools, based on the vertical geometric factor concept. The following example illustrates the geometric factor for thin bed response for a typical logging tool:
Given:
Bed Thickness = 4 ft, CONDb = 100 mmho/m, CONDs = 1000 mmho/m,
Gb = 0.728, CONDa = 100 * 0.728 + 1000 * 0.272 = 345 mmho/m The apparent conductivity is 3.45 times the actual conductivity of the zone (100 mmho/m), a 345% error, illustrating the large error inherent in typical induction log readings in thin beds. A resistive formation needs to be at least 24 feet thick for the vertical geometric factor to approach1.0.
Sample log presentations are shown I Figure 19.11. The shallow resistivity curve has evolved over time, from the 16” normal in the 1960’s, laterolog-8 (LL8) in the 1970’s, spherically focused log (SFL) in the 1980’s, to a shallow (10”) induction curve on the current array induction log. The newest array induction logs use multi-coils combined with higher transmitter currents, plus very intensive inverse modeling to obtain conductivity focused to 1, 2, or 4 feet. Commercial software is available to perform similar inverse modeling on older logs.
There are two major types of laterologs: three electrode guard systems and multiple electrode systems. Guard systems utilize two elongated focusing (guard) electrodes (A1 and A2 as in Figure 19.11) and a small center measure electrode A0. Zero potential difference is maintained between the center and guard electrodes during logging. Resistivity is proportional to the potential (voltage) on the center electrode, as shown mathematically below. Seven electrode systems have an additional two pairs of small electrodes placed symmetrically on both sides of the center electrode (M1 – M1’ and M2 – M2’). The zero potential difference is maintained between these additional electrodes. Seven electrode systems include the obsolete LL7 style tool. Dual Laterolog tools use 9 electrodes. Additional A1’ and A2’ electrodes provide greater guard electrode coverage than a single upper and lower guard. Different depths of investigation are created by controlling the potential on the outermost guard electrodes. The spherically focused log is also a 9 electrode system, but the electrodes are arranged to place the guards closer to the center electrode, and the equalizing electrodes further away (see Figure 19.14). In all guard systems, the zero potential difference between the center electrode and the guard electrodes prevents current emanating from the center electrode from flowing along the borehole even when it contains highly saline mud. Thus, the measure current will assume the shape of a cylindrical disc. The thickness of this current disc is approximately equal to the length of the center electrode plus one-half the distances separating it from each of the guard electrodes. In
both tool types, the current density varies inversely with
the radial distance and can be calculated from: Current density
= I / (2 * PI * r * t) Resistivity
of the formation is: Rt = K * V / I (same as ES log except
K is different)
The pseudo-geometrical factor concept was developed to estimate the influence of these zones on the measured apparent resistivities, in a manner similar to that described earlier for the induction log. Both borehole and bed thickness correction charts are available in service company chartbooks, based on computer models of the pseudo-geometrical factors for each tool design. Figure 19.13: Dual laterolog electrode arrangement.
Shaded area shows desired current paths. Guard electrodes
keep current focused.
The hybrid scale was run from 1950 into the 1970's. It is composed of a linear resistivity scale running from 0.0 on the left to 50 or 100 ohm-m in the middle of the track. From the middle of the track to the right hand margin, the curve is actually a linear conductivity scaled from 20 to 0 or 10 to 0 milli-mhos. These two scales are equivalent to a 50 to infinity or 100 to infinity resistivity scales. These combined curves give the hybrid scale a continuous resistivity range from 0 to infinity across one or two tracks. The conductivity curve was also presented on some logs. The hybrid scale was replaced by the logarithmic scale in the 1970's, which may have backup scales because of the high range of resistivity that can be measured with this tool. The SP curve may be present, but it may be pretty flat because laterologs were usually run in salt mud. The SP track may be shifted by splicing the film as the curve was recorded 28 feet off-depth on some tools. Newer logs usually have a gamma ray curve in Track 1 instead of the SP.
19.07
TOOL THEORY – MICRO
RESISTIVITY LOGS Figure 19.15 shows the Microlog electrode arrangement. Three small button electrodes (A, M1 and M2), spaced one inch apart, are embedded in the center of the insulated pad. A remote electrode, usually near the pad, is also used serving as the current return electrode B and voltage reference electrode N. Current electrode A is maintained at constant current intensity. The potential difference between electrodes M1 and M2 is used to derive a resistivity curve which is called the micro-inverse and is usually designated R1x1, or simply R1. The electrode arrangement for R1 is equivalent to a lateral-type resistivity tool having a depth of investigation of 1.5 inches. The potential difference between electrode M2 and the reference or remote electrode is used to derive a second resistivity curve called the micro-normal, usually designated R2. The electrode arrangement for R2 is equivalent to a normal resistivity tool and its 2 inch spacing gives it a depth of investigation of two to four inches. The Microlaterolog is a focused, pad-mounted shallow resistivity tool developed to overcome limitations of the Microlog in high resistivity formations and in salt mud situations. The tool design is similar to the Microlog with the exception of the electrode arrangement (see Figure 19.18). The electrode arrangement consists of a current electrode in the center surrounded by focusing electrodes embedded in an oil-filled rubber pad. A remote current return electrode is located near the pad. This electrode arrangement is similar to the seven electrode laterolog on a miniature scale. A voltage of constant intensity is applied to the center electrode while a controlled supply of current is applied to the focusing electrodes. The potential difference between the center electrode and the focusing or guard electrodes is maintained at zero by automatic controls. This has the effect of focusing the current into a narrow beam perpendicular to the pad and into the formation. The current beam maintains a uniform shape through the mud cake, spreading out as distance from the pad increases. The potential difference between the center electrode and the remote electrode, in combination with a calibration constant, is a measure of the apparent resistivity of a small volume of the formation near the borehole. The depth of investigation is about three inches from the tool pad. For mud cake less than 3/8 inch thick, the effect of mud cake on tool response is small and can generally be ignored. With flushed zone thickness of two to three inches. The tool reads flushed zone resistivity (Rxo) directly. In wells drilled with low resistivity (salt) muds, mud cake resistivity is usually quite low compared to flushed zone resistivity. Under these conditions the mud cake effect is still small for mud cake thickness greater than 3/8 inch. For fresher muds and higher Rmc/Rxo ratios, the 3/8 inch limitation applies. The Proximity log is a focused, pad-mounted tool and is a further development of the Microlaterolog to minimize mud cake effects. The tool design is very similar except for a modified guard electrode arrangement. A second ring of guard electrodes, in addition to those used in the Microlaterolog arrangement, is included. The beam electrode and the guard electrodes also have larger cross-section areas. This configuration, as illustrated in Figure 19.18 is referred to as a shielded guard device.
A voltage of constant intensity is applied to the beam electrode. A controlled supply of current is applied to the guard electrode to maintain zero potential between the shield and the beam electrode. The additional focusing shield constricts the current beam from the center electrode even more than with the Microlaterolog tool. A greater thickness of mud cake is thus penetrated with little change in the shape of the current beam from the center electrode. Measurement of the potential difference between the center electrode and the remote return electrode in combination with a calibration constant gives the resistivity of a small volume of the formation. The improved focusing gives the Proximity Log a greater depth of investigation and most of the tool response is received from a distance of six to ten inches from the pad. Field tests indicate that where moderate to deep invasion exists and sufficient flushing has occurred, reliable values for the flushed zone resistivity (Rxo) may be obtained.
The Micro Spherically Focused Log (MSFL) has superceded the Proximity log. It has the general electrode arrangement of the SFL described earlier, placed on a pad in miniature form. The MSFL is the current tool of choice for flushed zone Rxo measurement.
19.08
TOOL THEORY – SONIC
LOGS Hooke's Law, describing the behavior of elastic materials, states that within elastic limits, the resulting strain is proportional to the applied stress. Stress is the external force (pressure) applied per unit area, and strain is the fractional distortion which results because of the acting force. The modulus of elasticity is the ratio of stress to strain. Three types of deformation can result, depending upon the mode of acting force. The three elastic moduli are: Young's Modulus, Bulk Modulus, Shear Modulus, Where F/A is the force per unit area and dL/L, dV/V, and tanX are the fractional strains of length, volume, and shape, respectively. Another
important elastic constant, called Poisson's Ratio, is defined
as the ratio of strain in a perpendicular direction to the
strain in the direction of extensional force, The velocity of sound in a rock is related to the elastic properties of the rock/fluid mixture and its density, according to the Wood, Biot, and Gassmann equations. The
composite compressional bulk modulus of fluid in the pores (inverse
of fluid compressibility) is: ____1: Kf =
1/Cf = Sw / Cwtr + (1 - Sw) / Coil The pore space bulk
modulus (Kp) is derived from the porosity, fluid, and matrix
rock properties: The
composite rock/fluid compressional bulk modulus is: Compressional velocity (Vp) and shear
velocity (Vs) are defined as: Although it is not a precise solution, we often invert equations 5 and 6 to solve for Kb and N from sonic log compressional and shear travel time values. WHERE:
The Biot-Gassmann approach looks deceptively simple. However, the major
drawback to this approach is the difficulty in determining the
bulk moduli, particularly those of the empty rock frame (Kb and
N), which cannot be derived from log data. Murphy (1991)
provided equations for sandstone rocks (PHIe < 0.35) that
predict Kb and N from porosity: These can help overcome the lack of empty rock-frame data. An example of the Gassmann equation used to find sonic velocity in a gas filled rock can be found in Chapter Eighteen. NOTE: Abbreviations used in the literature for elastic constants vary dramatically and no consistent set was found. The abbreviations used in this book reflect those used in recent Schlumberger papers. CAUTION: This book uses the abbreviation "V" for Velocity AS WELL AS for Volume, as in Vsh for volume of shale (not velocity of shale or shear velocity). Likewise the abbreviation K is used for permeability (eg Kmax, Kv, Kh, etc) as well as for compressional bulk modulus. Watch the context. IMPORTANT NOTE: The mechanical properties theory is based on the assumption that rocks behave elastically and are isotropic. Neither of these assumptions is actually true in many situations. Anisotropic behaviour is common and fractured rocks may not behave elastically The nuts and bolts of the above equations shows three
things: It is the last fact that suggests that a log of acoustic velocity or specific acoustic travel time (sometimes called "slowness") might be a reasonable predictor of porosity. Sonic travel time is abbreviated as DELT in this book, and is often called "delta-T" in both spoken and written form.
This law applies to all electromagnetic waves as well as acoustic waves.
The critical angle is the angle of incidence that
creates refraction of sound energy along the interface between two
dissimilar media, for example along the wellbore face (as in well
logging) or along the boundary between two rock layers (as in
seismic refraction surveys). The equation is: Sonic logging tools consist of one or more sources of pulsed sound energy and a number of sound detectors. The sound travels from the source on the logging tool, through the mud in the borehole, to the rock. Here it is refracted at the critical angle, according to Snell’s Law, and travels in the rock parallel to the borehole. The source creates a compressional wave through the mud, a portion of which undergoes mode conversion to create a shear wave as well as the compressional wave in the rock. The shear wave is slower than the compressional, and modern sonic log processing can segregate and record both. See Figure 19.23 for a schematic diagram of the sonic log acoustic ray paths.
Velocity is derived from travel time by the equation: The inverse is also true: The conversion factor of 10^6 accounts for the conventional units of measurement on the sonic log – microseconds per meter (or foot). Acoustic travel time is also called slowness, and is sometimes called by its traditional abbreviation, delta-T, DT, or DELT. Don’t confuse sonic log Delta-T with normal moveout (NMO), which is also called delta-T when used in seismic data processing. The sonic log is usually presented as a log of acoustic travel time in units of microseconds per foot or per meter. Some sonic logs show a velocity scale, often non-linear. Another log presentation portrays the sonic data as its equivalent porosity, translated with a particular lithology assumption. The scales are usually called Sandstone or Limestone scales to reflect the assumption that was made to create them. Dolomite scales also exist on a few logs. The relationships are: 7: PHIS = (DELT - KS6) / (KS7 - KS6) Where: Sonic logging tools consist of a source of pulsed sound energy and a number of sound detectors. To understand the sonic log, we start with a description of the sources of acoustic energy, followed by a description of the sound waves created, ending with the tool arrangements and typical log presentations. Energy Sources for Acoustic Logs
1. Monopole sources emit sound energy in all directions radially from the tool axis. They are sometimes called axisymmetric or radially symmetric sources. Commercial wireline sonic logging tools, from the earliest tool to the present-day, carry a monopole source along with two or more monopole receivers. This tool arrangement creates the conventional compressional sonic log that we are all familiar with. Sound energy from the source that reaches the rock at the critical angle is refracted (bent) so that it travels parallel to the borehole inside the rock. This energy is refracted back into the borehole, and strikes the receivers. The difference in time between arrivals at the receivers is used to estimate the travel time, or slowness, of sound in rock. Sound velocity is the inverse of slowness. In fast formations, this tool design can also receive shear waves generated in the formation, where some of the compressional energy is converted to shear energy. A fast formation is a rock in which the shear velocity is faster than the compressional velocity of the fluid in the borehole. A slow formation is a rock in which the shear velocity is equal to or slower than the fluid velocity. The monopole source also generates a shear wave on the borehole surface in fast formations, called a pseudo-Rayleigh wave. The converted shear and the pseudo-Rayleigh arrive at the monopole detector with nearly the same velocity and cannot usually be separated. Monopole sources also generate the Stoneley wave in both fast and slow formations. The low frequency component of the Stoneley is called the tube wave. More detailed descriptions of all wave modes are given later in this Chapter. 2. Dipole sources and receivers are a newer invention. They emit energy along a single direction instead of radially. These have been called asymmetric or non-axisymmetric sources. They can generate a compressional wave in the formation, not usually detected except in large boreholes or very slow formations. They generate a strong shear wave in both slow and fast formations. This wave is called a flexural or bender wave and travels on the borehole wall (Figure 19.18). Unlike the pseudo-Rayleigh from a monopole source, which also travels on the borehole wall at near shear velocity, the flexural wave field is asymmetric.
Modern open-hole sonic logging tools carry both monopole and dipole sources and receivers so that compressional and shear arrivals can be recorded in slow and fast formations. The sources are fired alternately; the sound from one source will not interfere with the other. Some modern sonic logging tools have two sets of dipole sources set orthogonally, with corresponding dipole receivers. Shear data can be recorded in two directions in the formation. These are called crossed-dipole tools. After suitable processing, the two acoustic velocity measurements are translated into a minimum and maximum velocity. The ratio of these velocities is a measure of acoustic anisotropy in the formation. This is an important property in formation stress analysis, hydraulic fracture design, fractured reservoir description, and tectonic studies.
Figure 19.20 (upper) shows a waveform from a monopole source in a slow formation. There is a compressional wave (P) but no shear arrival. The dipole waveform (lower) at the same depth shows no compressional but good shear (S) arrivals. Notice that the shear wave arrives after the fluid wave (the definition of a slow formation). In a fast formation, the shear arrival will be seen on the monopole waveform (Figure 19.19.05) as well as on the dipole waveform.
While there are strong collar arrivals on monopole LWD tools, there have been monopole LWD sonic logs operating successfully for many years, using various mechanical and processing techniques to attenuate the collar arrival. For LWD dipole tools, the collar mode interferes with the formation dipole, forming coupled modes where the formation shear speed is difficult to extract. Dispersion Compressional waves have very little dispersion. The various wave modes used to measure shear velocity are very dispersive, which may account for errors in shear velocity on older logging tools, when high frequency sources were the norm. Today, tools are designed to work below 5 KHz for shear measurements, instead of 20 to 30 KHz on older tools. Typical theoretical dispersion curves for a particular velocity assumption are shown in Figure 19.21 to illustrate the problem. For larger boreholes and/or slower formations, the dispersion curves shift to lower frequencies.
Acoustic Transmission Modes from a
Monopole Sources Monopole sources can develop both body and surface waves; dipole and quadrupole sources create only surface waves. Body waves travel in the body of the rock. Surface waves travel on the borehole wall or bounce from the wall to the tool and back to the wall. The surface waves are also called guided waves or boundary waves. 1. Fast compressional waves , also called dilational, longitudinal, pressure, primary, or P-waves are recorded by all monopole sonic logs, beginning in the mid to late 1950's. They are the fastest acoustic waves and arrive first on the sonic wavetrain. Biot called these dilational waves of the first kind and are body wave. The velocity of this wave is related to the elastic properties of the formation rock and fluid in the pores. It has been used successfully for years as a porosity indicator. The compressional wave is initiated by a monopole energy source and is transmitted through the drilling mud in all directions. Sound traveling at the critical angle will be refracted into the formation, which in turn radiates sound energy back into the mud, again by refraction. The sound waves refracted back into the borehole are called head waves. The compressional head wave is detected by acoustic receivers on the logging tool. A dipole source generates a noticeable compressional wave in slow formations and in large boreholes, especially on tools running at higher frequencies. The wave is probably present in faster formations and smaller boreholes, but is below the detection level of most processing techniques (see Figure 19.20). The velocity of the compressional wave does not vary much with the frequency of the wave. The frequency spectrum of the wave depends on the source frequency spectrum and is usually in the 5 to 30 KHz range. Older tools generally used the higher frequencies, current tools use the lower. An acoustic ray path is a line that traces the path that the sound takes to get from the source to the receiver. Compressional waves vibrate parallel to their ray path. 2. Slow compressional waves are transmitted, as well as the fast waves described above. It is called a dilational wave of the second kind by Biot. It is also a body wave and travels in the fluid in the pores at a velocity less than that of the fast compressional wave in the formation fluid. Its amplitude decays rapidly with distance, turning into heat before it can be detected by a typical sonic log. No pores, no fluid, no slow compressional wave. Although predicted by Biot in 1952, it was not detected in the lab until 1982 by Johnson and Plona. I am not aware of any practical use for this velocity in the petroleum industry. The slow and fast compressional waves as described above should not be confused with the slow and fast velocities found by crossed-dipole sonic logs in anisotropically stressed formations. 3. Surface compressional waves , also called leaky compressional, compressional "normal mode", or PL waves, follow the fast compressional wave. This is a surface wave from a monopole source and travels on the borehole wall. Amplitude varies with Poisson's Ratio of the rock/fluid mixture. It is present in both fast and slow formations.
The wave is dispersive, that is, low frequencies travel faster than high frequencies. It has velocities that range between the fast compressional wave through the formation (Vp) and the fluid wave in the borehole (Vf). The first arrival coincides with Vp and the balance of the wave shows up as a "ringing" tail on the compressional segment of the wavetrain. It usually decays to near zero amplitude before the shear body wave arrives. This monopole leaky compressional wave is strongest in very slow formations, large boreholes, and boreholes with significant near-borehole mechanical damage. The number of normal modes depends on source frequency; if frequency is too low, there will be no surface compressional wave. The first normal mode is sometimes called the least normal mode. 4. Shear body waves , also called transverse, rotational, distortional, secondary, or S-waves, are generated by conversion of the compressional fluid wave when it refracts into the rock from the wellbore. It converts back to a P wave when it refracts through the borehole to reach the sonic log detector. This wave is also a body wave. The refracted wave returning to the logging tool is called the shear head wave. Shear waves vibrate at right angles to the ray path. Monopole sonic logs cannot detect a body shear wave in a slow formation (Vs < Vf) because refraction cannot occur. The modern dipole sonic log can generate a shear wave in all formations, but the shear wave is actually a surface wave called a flexural wave. A quadrupole source generates what is known as a screw wave with the same result. When shear is missing on a conventional monopole log (and there is no dipole shear data), it can be estimated by a transform of the Stoneley wave velocity. However, the empirical formula ignores many of the minor variables, so the method is not very accurate. Shear waves travel at a slower rate than compressional waves. Compressional velocity is approximately 1.6 to 1.9 times higher than shear velocity in consolidated rocks but the ratio can rise to 4 or 5 in unconsolidated sediments. Shear velocity at sonic log frequencies is not very dispersive but the wave modes used to measure shear velocity are highly dispersive. Low frequency components are faster than high frequency components (see Figure 19.19.04). Because even low frequency logging tool sources have a moderate frequency spectrum, the shear body wave will show the "ringing tail" effect on the shear arrival. Dispersion is important to us for another reason. Lab measured sonic velocities are made at high frequency, usually 1 MHz, and logs make their measurements at low frequency, 3 to 30 KHz, so comparisons of the results from lab and log measurements is difficult. The shear wave velocity from a sonic log can be used to predict porosity just like the compressional wave. This is not true for 1 MHz lab measurements because the wavelength is too small to treat the rock/porosity mixture as a single coupled material. Shear velocity is relatively independent of fluid type, so there is no appreciable gas effect on the measurement, unlike the compressional wave, which has a large gas effect. Combined with compressional wave velocity and density data, all the elastic properties of the rock can be computed. Similarly, at seismic frequencies, the shear wave is not significantly affected by the fluid type in a rock so, like the shear sonic log, there is no gas effect on the shear seismic section. Thus, a gas related bright spot (direct hydrocarbon indicator or DHI) on a compressional wave seismic section will have no comparable shear wave anomaly. In contrast, a lithology related anomaly will have a corresponding shear wave anomaly. Thus, it is possible to use shear wave seismic data to evaluate the validity of direct hydrocarbon indicators. 5. Shear surface waves , also called pseudo-Rayleigh, multiple-reflected conical, reflected conical, or shear "normal mode" waves, follow the shear body wave. They are a surface wave generated by a monopole source. They are also classified as a guided-wave. Monopole sonic logs cannot generate a surface shear wave in slow formations for the same reason that they cannot generate a body shear wave. Dipole sonic logs can generate a different form of shear surface wave, the flexural wave, but cannot create the shear body wave. These waves have also been called slow shear waves and shear waves of the second kind in a few papers. This usage should not be confused with the slow and fast shear velocity found by crossed-dipole sonic logs in anisotropically stressed formations. These are called pseudo-Rayleigh waves because the particle motion is similar to a Rayleigh wave on the Earth's surface, but it is confined to the borehole surface. It may also be called a tube wave as it travels on the tubular surface formed by the borehole wall. This latter terminology can be confusing because Stoneley and Lamb waves are also called tube waves. Surface waves on the Earth include Rayleigh and Love waves. Particles in Rayleigh waves vibrate vertically in elliptical retrograde motion and cause severe damage during earthquakes. They are also the principal component of ground roll in seismic exploration. Love waves vibrate horizontally, similar to a shear wave, and can be considered as a surface shear wave when found on the Earth's surface. The number of normal modes depends on source frequency; if frequency is too low, there will be no pseudo-Rayleigh wave. The first normal mode is sometimes called the least normal (shear) mode. This wave is dispersive, that is, low frequencies travel faster than high frequencies. The lowest frequency component arrives at shear velocity (Vs) and reinforces the shear head wave arrival, if one exists. The balance of the energy is dispersed over the interval between shear wave velocity (Vs) and fluid velocity (Vf). The Airy phase of the shear normal mode (pseudo-Rayleigh) occurs just after the fluid wave. It can distort the surface shear wave and make it difficult to determine shear velocity. It can also distort the fluid wave and the Stoneley wave arrivals. I am not aware of any practical use for this part of the waveform in the petroleum industry, but it is mentioned often enough |
Thus, analysis of log data is required. The art and
science of log analysis is mainly directed at reducing a large
volume of data to more manageable results, and reducing the
possible error in the assumptions and in the results based
on them. When log analysis is combined with other physical
measurements on the rocks, such as core analysis or petrographic
data, the work is called petrophysics or petrophysical analysis.
The results of the analysis are called petrophysical properties
or mappable reservoir properties. The petrophysical analysis
is said to be “calibrated” when the porosity, fluid
saturation, and permeability results compare favourably with
core analysis data. Further confirmation of petrophysical properties
is obtained by production tests of the reservoir intervals.
Figure 19.10A: Schematic diagram of
simplified 2-coil induction log, equivalent to a mine detector
or hand-held metal detector. Real tools have 5, 6, or more
transmitters – receiver
pairs to focus the current path.
The path taken by the measure current of a laterolog
constitutes a series circuit through the drilling mud, mud
cake, flushed and invaded zones, and the undisturbed formation.
In a series circuit, the total resistivity is the sum of resistivities
along the current path. 
Figure 19.17: Direction of pressure waves from (left
to right) monopole, dipole, and quadrupole sources (from
Zemanek et al, 1991)
Figure 19.22: Waveform from a monopole source in a
fast formation, showing some of the definitions used in the
literature (from Paillet, 1991)