A hadron is any
strongly interacting composite subatomic particle.
All hadrons are composed of quarks. Hadrons are
divided into two classes. Baryons are strongly
interacting fermions such as neutrons and protons,
made up of three quarks. Mesons are strongly
interacting bosons consisting of a quark and an
antiquark.
CRAIN'S
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c. 1978 - 2008 E. R. (Ross) Crain, P.Eng.
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CHAPTER EIGHTEEN: PHYSICAL PROPERTIES OF ROCKS AND FLUIDS Table
of Contents TABLE 18.01 Physical Properties of Rock Publication History: This Chapter formed Appendix Three of The Log Analysis Handbook, Pennwell, 1986. The sections on resistivity concepts in this Chapter are patterned after material in "Basic Concepts of Well Log Interpretation", published by Welex in 1980. The sections on photo electric effect, thermal neutron decay time, gamma ray response, and the response of real neutron logs is abridged from "Radioactive Logging Parameters for Common Minerals", by H. Edmundson, L. L. Raymer, CWLS and SPWLA, 1979. The balance of the Chapter is from a research project undertaken while employed by J. C. Sproule and Associates Ltd in 1969 for Riley’s DataShare International and subsequent technical paper, "Prediction of Log Interpretation Parameters - An Independent Study", by E. R. Crain, published in 1971 by CWLS. Secion 18.01 updated March 2008. CHAPTER EIGHTEEN: PHYSICAL PROPERTIES OF ROCKS AND FLUIDS 18.00
Introduction to This Chapter The object is to provide methods for estimating some basic rock properties, as well as to give methods for combining known data to obtain values for mixtures. Methods covered include resistivity, density, acoustic velocity, gamma ray, neutron, photoelectric effect, and thermal decay time response in rocks. A few initial definitions are in order. A law can be proved, using the most primitive of physical or mathematical rules, whereas a theory cannot be proved. For example, the Law of Conservation of Energy can be proved by invoking more primitive physical laws. The Theory of Relativity cannot yet be proved, and alternate theories exist, although they are not widely held. A good theory explains all the known data, and may even predict as yet unobserved data, as the Theory of Relativity has done. A poor theory may still be widely believed, even if it fails to account for all observed facts. Some believers may discount the data that does not fit, assuming it is in error, or will predict that improvements to the theory will allow all data to fit. The controversy over Creation (now known as Intelligent Design) versus Evolution falls into this category. An empirical relationship differs from both a law and a theory. The empirical relationship is a mathematical "best fit" between two or more observed sets of data. Many individual data sets will not follow the empirical relationship well. For example, it is often true that a larger object weighs more than a smaller item, but there are many exceptions to that rule. These
relationships are often termed rules of thumb, and frequently
apply only in limited areas or under very restrictive circumstances.
Some relationships used in log analysis are actually laws, such
as those dealing with the summation of densities in mixtures.
Many, if not most, are empirical relationships, such as the Wyllie
time-average formula, or the Archie formation factor concept.
18.01
Basic Physics and Chemistry
More recently, nuclear physicists have proposed the "Standard Model", showning that these so-called "basic particles" are actually made of even smaller basic particles, called naturally enough, sub-atomc particles. Below is the current list:  QUARKS
Abbrev Elec Charge Mass Up u +2/3 2 MeV Stable Down d -1/3 5 MeV Stable Two Up quarks and 1 Down quark make a Proton with net charge of +1. Two Down quarks and 1 Up quark make a Neutron with net charge of 0. Charm C +2/3 1.25 GeV Unstable Strange S - 1/3 95 MeV Unstable Top t +2/3 171 GeV Unstable Bottom b -1/3 4.2 GeV Unstable The unstable quarks make up short-lived particles, seen only in very high energy physics labs and cosmic rays.
 LEPTONS Abbrev Elec Charge
Mass Electron e -1 0.511 MeV Stable Muon u -1 105 MeV Unstable Tau T -1 1.78 GeV Unstable e . There are three neutrinos corresponding to each of the three leptons. Neutrinos have no charge and rarely interact with ordinary matter.
There are antiparticle equivalents to the quarks and leptons. Antiparticles are subatomic particles, such as positrons, antiprotons, or antineutrons, having the same mass, average lifetime, spin, magnitude of magnetic moment, and magnitude of electric charge as the particle to which they correspond, but having the opposite sign of electric charge, opposite intrinsic parity, and opposite direction of magnetic moment. They exist today only in high energy particle accelerators but were abundant, in theory, in the early moments of the Big Bang . The forces that act to bind or attract particles are transmitted by other particles, called Bosons. The most obvious boson is the photon, the carrier of electromagnetic radiation (eg: light, radio, television, gamma rays, X-rays). Photons can have an effect over huge distances. Photons can behave as partcles or waves, leading to a duality that underlies much of quantum physics. The Z boson, W- boson, and W+ boson operate over very tiny inter-atomic distances (10^-18 meters), carrying the weak force.
Gluons come in eight different species. They carry the strong force that binds quarks into other particles. All the particles mentioned so far have been discovered or proven to exist in the laboratory. The Higgs particle (graviton) is postulated but as yet not proven to exist. It could account for the "missing mass" or "dark matter" problem haunting current cosmological theories. An atom consists of at least one proton and one electron (hydrogen) The nucleus of all other atoms consists of protons and neutrons, surrounded by electrons. An element is made of one or more atoms with the same number of protons. An element cannot be broken into smaller elements by ordinary chemical processes. Helium, oxygen, sodium or chlorine are elements. There are 117 elements known to date, the heaviest being unstable and very short-lived. Unstable elements are said to be radioactive, decaying in time to some lighter, more stable element.
The atomic number (Z) represents the number of
protons in an atom and uniquely identifies a
chemical element. The number of electrons
surrounding the nucleus equals the number of
protons.
The atomic weight (A), or mass number, is the number of protons plus neutrons in the nucleus of an atom. Isotopes of an element have the same number of protons and electrons, but different numbers of neutrons. Some isotopes are stable, some are radioactive. About 339 isotopes occur naturally on Earth, of which about 79% are stable. Counting the radioactive isotopes not found in nature that have been created artificially, more than 3100 are currently known For example, 93% of potassium atoms have 19 protons with 20 neutron and are stable, giving an atomic number of 19 and an atomic weight of 39. One particular isotope has 21 neutrons, giving an atomic weight of 40. It is unstable and comprises only 0.012% of all Potassium atoms. Other isotopes, some stable, some not, make up the remaining 7% of the atoms. The common forms of radioactive decay are by emitting Alpha, Beta, or Gamma particles (or rays), Alpha decay is a type of radioactive decay in which two protons and two neutrons are emitted. They are bound together into a particle identical to a helium nucleus. The original atom transforms into an atom with a mass number 4 less and atomic number 2 less. A common example is the decay of Uranium-238 into Thorium-234. Two electrons are also stripped from the original atom. Excess energy is released as one or more gamma rays. Alpha particles are heavy and cannot travel any significant distance.
A third form of Beta decay, called Inverse Beta, or Electron Capture, converts a proton to a neutron by capturing an inner shell electron, and emitting the excess energy as a low energy gamma ray (X-ray). For Potassium-40, this mode of decay also results in stable Argon-40. Since K-40 has a half-life of more than a billion years, gamma rays are constantly being produced and can be detected by conventional instrumentation. Beta particles cannot travel far and are not particularly dangerous unless ingested.
Gamma rays are
high energy photons,
a form of
electromagnetic
radiationof
frequencies produced
by sub-atomic
particle
interactions, such
as electron-positron
annihilation or
radioactive decay.
Gamma rays are
generally
characterized as
having the highest
frequency and
energy, and also the
shortest wavelength
(below about 10
picometers).
Hard X-rays overlap the range of long-wavelength (lower energy) gamma rays, however the distinction between the two terms depends on the source of the radiation, not its wavelength; X-ray photons are generated by energetic electron processes, gamma rays by transitions within atomic nuclei. Due to their high energy content, gamma rays can cause serious damage when absorbed by living cells.
Elements are sorted into ascending order of atomic number, in a structured table called the Periodic Table. The table is arranged so that elements with similar chemical properties (same number of valence electrons in their outer shell) are aligned vertically. Vertical columns are called Groups or Families. Horixontal rows represent the number of electron shells filled or partially filled. For handy reference, a periodic table of the elements is presented below, taken from Wikipedia. Click on element symbol to see detailed description, atomic weight, and other important details. Standard periodic table
A molecule is a sufficiently stable, electrically neutral, assemblage of two or more atoms held together by strong chemical bonds. A chemical compound is a combination of two or more elements or molecules, such as quartz, a combination of silicon and oxygen, or dolomite, a compound of calcium, magnesium, sulphur, and oxygen. Water is a compound of hydrogen and oxygen. There are two basic kinds of compounds: ionic and covalent. Ionic compounds are held together by electrostatic attraction between positive and negative ions, for example NaCl (sodium chloride, halite, rock salt) or CaCO3 (calcium, carbonate, calcite, limestone). Covalent compounds are held together by sharing electrons, such as H2 (hydrogen), O3 (ozone), CH4 (methane), H2O (water). The sharing of free electrons in metals, called metallic bonding, is similar in concept to ionic bonding. Many compounds have bonding that is a combination of covalent and ionic. A mixture is a physical combination of a minimum of two elements or compounds. No chemical reactions take place between the mixed components. For example, sandstone is a mixture of quartz, water and/or oil and/or gas, and/or other constituents such as clay, silt, or any other rock mixtures. Salt dissolved in water is also a mixture. When a compound is formed from two or more elements, the volume of the resulting molecule may be more or less than the original components. However, the total weight or mass, will not change, providing all gases formed, if any, are retained. When a physical mixture is created, such as sand grains and water, the volume of the resulting mixture is the sum of the volumes of the original components, provided any gases involved, such as air between sand grains, are retained, and held at a constant temperature and pressure. The mass again will remain the sum of the masses of the individual components.
WHERE: The unit of resistance is the Ohm, named after 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 unity. This point is illustrated in Figure 18.01. Thus: WHERE:
Conductance
is the inverse of resistance: WHERE: Units of conductance are measured in Siemens, and are 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 (mS/m), where milli stands for 1/1000. Many people neglect to write or say the "per meter" part of the units when referring to conductivity and the "meter" part of resistivity. Do not confuse resistivity with resistance just because the units have been incorrectly or inadvertently abbreviated. When
combining the effects of two or more resistances or resistivities,
one must distinguish between series and parallel circuits, as
shown in Figure 18.02. The total resistance or resistivity of
items connected in series, is the sum of their resistances or
resistivities:
The
total resistance of resistances connected in parallel is the inverse
of the sum of the inverse of each resistance. This
is more easily seen as the inverse of the sum of the conductance. These relationships are laws of physics within the pressure and temperature domain of interest to log analysts. Superconductivity does not occur in our realm. Resistivity is summed in the same manner as resistance - that is, the laws for series and parallel circuits must be obeyed. Example: RTOTAL = 1 + 10 = 11 ohm C = 1/R = 0.9 siemens RES1
= 1 ohm-m RESTOTAL = 1 + 10 = 11 ohm-m COND = 1 / RES = 0.9 siemens/m
RTOTAL = 1 / (1 / 1 + 1 / 10) = 0.9 ohm C = 1 / R = 1.1 siemens RES1
= 1 ohm-m RESTOTAL = 0.90 ohm-m COND = 1.1 siemens/m
Pure water is also a very poor conductor. However, if salt is added to water, the solution becomes more conductive. Current is conducted through water by ions formed from the salt in solution in the water. The more ions present in the solution, the more conductive the solution will be. Since most natural waters in rocks contain salts of various kinds, the majority of natural waters are conductive. To develop an understanding of how logging systems respond to various types of rocks the manner in which pores are interconnected must be visualized. The simplest system to imagine is an unconsolidated sand as shown in Figure 18.03. In such a rock, the sand grains are piled on top of each other and the pore system is the space remaining between grains.
The grains may or may not be of uniform shape and size and packing. Cementing material may bind the particles together. All of these conditions would affect the pore system. Some other types of pores are also shown in Figure 18.03. Thus, the distribution of pores in various rock types are not uniform, but dependent upon the genetic origin of the rock and the subsequent geologic changes to which it has been subjected. Using
the methods already developed, the equation for the resistance
of a one meter cube to current flow through two parallel faces
can be written. If
length and area both equal 1, then: WHERE: The resistance, in ohms, of a one meter cube of water is numerically equal to the resistivity of the water in ohm-meters. This is true for any material or combination of materials and is not restricted only to water. See Figure 18.04.
Now consider a one meter cube of rock that is 100% water saturated, that is, all the pores are filled with water. Resistivity of the cube may be written in terms of the current path length, area and resistivity. The
resistivity of the current path is RW and the path length (Le1)
is at least one meter, but probably longer. The area is proportional
to porosity. Thus: WHERE: This relationship will be developed further in the following section.
In
terms of the cubes developed, F becomes: WHERE: From laboratory measurements made on rock samples it has been found that formation factor remains constant for a wide range of water resistivity values, as shown in the top half of Figure 18.05.
Consider
a cube of rock containing water and a hydrocarbon. Then: WHERE: Resistivity
index is the ratio of true resistivity of the rock, to the resistivity
of 100% water saturated rock , which was derived in the previous
section. Thus: Using
the cubes already defined, the resistivity index becomes: WHERE: This indicates that the resistivity index varies with a number of rock properties. The graphical representation of this is shown in the bottom of Figure 18.05.
Much work has been done to develop empirical relationships between water resistivity, porosity and water saturation. G.E. Archie published a paper in the 1942 transactions of AIME entitled "The Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics". The empirical relationships which he presented are still the most widely used today and are referred to as the Archie Equations. First,
he showed with core samples, as we have previously defined, that
formation resistivity factor, water resistivity and rock resistivity
are related by the following expression over wide ranges of porosity: WHERE: Second,
he showed that measured formation factor and porosity are related
by the general expression: WHERE: The formula applies for wide ranges of porosity of the same rock type. The exponent is referred to as the cementation factor or the cementation exponent. Depending on the rock type, the value for M varies from approximately 1.3 to 2.3. The exponent M seems to be a function of the degree of cementation in clastic rocks. Finally,
Archie stated that water saturation is related to the rock resistivity
by the expression: WHERE: The exponent N is referred to as the saturation exponent, and is generally considered to have a value near 2.0. These empirical relationships eliminate the need to know the effective path lengths described earlier. Note that Ro / Rt in the above equation is the inverse of the resistivity index (RI). Archie's
equations are summarized as follows: WHERE: These equations are the basis for most resistivity log interpretation methods in use today, with the exception of very shaly sandstones. The
Winsauer porosity equation was developed as a result of a study
on the formation factor porosity relationship of many different
sandstones by W.O. Winsauer, H.M. Shearin, Jr., P.H. Masson, and
M. Williams. It was published in 1952 in the Bulletin of the AAPG,
in a paper entitled "Resistivity of Brine Saturated Sands
in Relation of Pore Geometry". They concluded that, for the
rocks studied, an expression of the following form described their
experimental data: WHERE: They
evaluated A and M in terms of their data with the following result: WHERE: The Winsauer equation is widely used today for the evaluation of sandstones from resistivity logs. The unmodified Archie formula with A = 1.0 and M = 2.0 is often used in carbonates. Most analysts prefer to find values of A and M for the particular rocks they are evaluating. This is described more fully within in this book. It
is often necessary to compute porosity from the formation factor,
by inverting the Archie or Winsauer equation: WHERE: These formulae pervade the porosity - water saturation literature, as well as previous Chapters of this book. Example: 2.
Formation Factor from Porosity (Archie): 3.
Porosity from Formation Factor (Archie): 4.
Water Saturation (Archie): OR
F = 10 / 0.1 = 100
6.
Porosity from Formation Factor (Winsauer):
The following material, which summarizes the scene very effectively, has been condensed from "The Evaluation of Shaly-Sand Concepts in Reservoir Evaluation", by P. E. Worthington, published by SPWLA in the Log Analyst for Jan-Feb, 1985. "The
emergence of the shaly-sand problem as it affects resistivity
data can be more readily traced by considering only conditions
of full water saturation in the first instance. A convenient starting
point is the definition of formation factor F which was first
of three equations proposed by Archie, namely: WHERE: A plot of Co vs CW for a given sample should furnish a straight line of gradient 1/F provided that Archie's experimental conditions of a clean reservoir rock fully saturated with brine are completely satisfied. Subject to these conditions the formation factor is precisely what the name implies; it is a parameter of the formation, more specifically one that describes the pore geometry. It is independent of CW so that a plot of CW/Co vs CW for a given sample should furnish a straight line parallel to the CW axis, as in Figure 18.06A.
However, around 1950 there was increasing evidence from various formations to suggest that the ratio CW/Co is not always a constant for a given sample but can actually decrease as CW decreases. The relative decrease in CW/Co at a given level of CW appeared to be more pronounced for shalier specimens. Since CW was presumed to be known, the only possible explanation for this phenomenon lay in the effect of the shale component of the reservoir rock upon Co. This effect was essentially to under reduce Co as CW decreased or, to put it another way, to impart an extra conductivity to the system at lower values of CW. For this reason the electrical manifestation of shale effects has been described in terms of an "excess of conductivity." It became advisable to regard the ratio CW/Co as an apparent formation factor Fa which is equal to the intrinsic formation factor F only when Archie's assumptions are satisfied. Since
the Archie equation was not found to be valid for all formations,
a more general relationship between Co and Cw was sought in order
to accommodate the excess conductivity. By rewriting the Archie
equation and incorporating the excess conductivity within a composite
shale-conductivity term X, it was proposed that an expression
of the following form is valid for all granular reservoirs that
are fully water saturated. WHERE: For a clean sand, X approaches 0.0 and the equation reduces to Archie's. If CW is very large, X has comparatively little influence on Co and again it effectively reduces to the Archie definition. Conversely, the ratio CW/Co is effectively equal to the intrinsic formation factor F only if X is sufficiently small and/or CW is sufficiently large. Thus, although the absolute value of X can be seen as an electrical parameter of shaliness, the manifestation of shale effects from an electrical standpoint is also controlled by the value of X relative to the term CW/F. During the period 1950-1955 evidence began to accumulate that the absolute value of the quantity X is not always a constant for a given sample over the experimentally attainable range of CW but can vary with electrolyte conductivity. The most widely accepted behavioral pattern, which has continued to be supported, was that for a given sample, the absolute value of X increases with CW to some plateau level and then remains constant as CW is increased still further. This pattern is illustrated for hypothetical data in Figure 18.06B. Here the terms "non-linear zone" and "linear zone" have been adopted for the regions of variable X and constant X, respectively. It was often the practice to estimate porosity from the ratio CW/Co using a standard version of Archie's second equation in conjunction with resistivity logging data from nearby water zones. In so doing it was essential to have sufficiently clean conditions for there to be a well defined relationship between porosity and CW/Co. Where this condition was satisfied it was still possible to proceed even if the ratio CW/Co actually represented an apparent formation factor Fa instead of the intrinsic formation factor F. In the former case A and M would be pseudo-parameters which would compensate | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Beta emission is a process in which an electron
and an antineutrino (or a positron and a neutrino)
are emitted. In the case of electron emission, a
neutron is converted to a proton and is referred to
as "beta minus", while in the case of a positron
emission a proton is converted into a neutron and is
called "beta plus". For Potasium-40, beta-minus
ewsults in Calcium-40 and Beta-plus in Argon-40.
Both daughter products are stable.
