Earth
Mechanical Systems Science applies directly
to Drilling Reservoirs
and Geomechanics
The Forces that govern Earth Mechanics are a small subset
of Universal physical laws!
( Note: There are special conventions used in this
file. Square brackets [ ] encompass physically meaningful
terms that are conserved; for instance [ mass-energy]
; [stress/
strain];
and [ mass-energy-space-time].
Words that have rigorous physical meanings have color
codes. The color codes highlight rigorous mechanical
and conservation law terms that overlap with much looser
language terms. Wherever not specified, assume that
the more rigorous physical definition is intended.
When deterministic physical
laws and related definitions are used, conclusions are
much stronger.
Mass
and energy
are conserved as such in the laboratory, the
earth, and the Universe. A specific cross-referencing
of [mechanical terms]
between the laboratory and the earth is shown in Comparison
of Laboratory and in situ Rock Mechanics systems.
Synthesis of
accepted physical laws explains Earth
Mechanics and Pore Pressure.
[Mass-energyy]
synthesis inside the earth's crust is a significant
advance in physical science. Great scientists applied
conservation laws and discovered new physical laws.
Newton and Einstein discovered closed-form [ mass-energy]
conserved laws that apply on and above the earth. There
is a compatible mathematical solution that seems to
apply within the earth.
Pore pressure
and effective stress are potential
energies in the earth's sedimentary
crust. The sum of two-phase energy
is generated and regulated by overburden
mass.
Overburden mass is fluid
and mineral
mass that
is integrated over depth. Grain-matrix
strain coincides with solid
mass conservation.
Grain-matrix strain
is also the mathematical complement of measurable porosity.
It denotes fluid
and solid mineral
partitioning. There are three closed-form solutions
for these physical, geologic, and mechanical
terms that conserves [ mass-energy]!
The physical explanation of earth forces is a summation
of physical and conservation laws in the earth. These
laws act in conjunction with the earth's own gravity.
[Mass-energy]
is thereby explicitly conserved within our three-dimensional,
solid-liquid
phase planet!!
These two books are a significant advance
in physical science that now includes the
mechanics inside of our earth. RETURN
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About
the book covers: The laws of Newton, Hooke,
and Coulomb were discovered before 1800. Their
laws were combined using a few applicable conservation
laws to define Pore
Pressure through Earth Mechanical Systems;
The Force Balanced Physics of the Earth's Sedimentary
Crust . The fluid in a borehole (Pb) presses against
the natural Pore pressure
(PP)
and fracture pressure (Pf) forces in the earth at the
borehole wall. Unbalanced forces can cause loss of circulation
and/or well blowout disasters.
More recently, "Deterministic
Earth Mechanical Science" was written
to explain the macro-mechanics revealed in the first
book. "Molecular mechanics"
bridges and explains the conceptual gap between Newtonian
macro-mechanics and quantum mechanics. It also provides
a much broader deterministic explanations of the great
questions of earth science.
The newer book's cover is shown on the left above.
The first two essays in News
give the most up to date physical explanations on the
whole of Deterministic Earth Mechanical Science. A Physical
Law Synthesis that Explains Earth Mechanics covers the
highlights. Each of the aforementioned book's list of
chapters can be seen by clicking on the book's titles
above. Each book also has a short list of keywords and
a glossary of important mechanical terms.
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Hyperlinks
within the website related Earth Mechanical Systems
Subjects
Earth
mechanical systems rigorously explain a great deal about
geology. They explain earth physiography
and quantify the forces involved in continental drift.
The earth's [ mass-energy
] conservation laws are given and explained. The earth's
mechanical limits triangle describes the earth's
mechanical [stress/strain] limits using equivalent [mass-energy]
conservation laws. The question, "Why learn
about the earth's [two-phase]
mechanics? " is asked and answered. A very short
abstract touches the highest points. A longer synopsis
covers the most important scientific points. Feel
free to contact phil@force-balanced.net
with short questions and/or book orders.
______________________________________________________
Earth
mechanical systems are a unifying concept that has eluded
earth scientists for over 200 years. The minerals
and fluid
that compose the earth are the medium. Physical laws
are the mechanisms. The medium and mechanisms are a
continuous [mass-energy] conserved field. Einstein and
Newton's syntheses describes a [mass-energy-space-time]
continuum of which the earth's interior is now a part.
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"Pore
pressure through Earth Mechanical Systems",
describes a very important special case of mass-energyconservation
law physics. The force of its own gravity operates in
concert with other conservation laws in our 3-dimensional
earth. Electrostatic repulsion of adjacent molecular
electron clouds keep the earth from collapsing to the
size of a marble.
The mineral
and fluid
molecular phases of the earth generate, bear, and transmit
all the loads. Stress and strain
have solid mass conservation
and porosity
in common. The correlations of stress, fluid
pressure and physical properties through
conservation laws are shown and explained in the first
book.
The Chapters in the first book; 1) - Explain the
above mentioned globally applicable controlling physics
with respect to rock, mineral,
and fluid
physical properties. 2) - Details mineralogic
inter- and intra-particle controls of sediment compaction.
3) - Mineral specific compaction curves are demonstrated
to be [stress/strain] causal relationships. 4) - Presents
data that demonstrates differential stress
minimization in normal-fault and strike-slip
tectonic regimes. 5) - Describes the interactions of
petrophysical instruments with minerals,
fluid
and porosity. 6)- Explains earth
mechanics as a continuous [stress,
fluid pressure
] / [mass-mineralogic
strain] field. 7) - Demonstrates that
fracture pressure
regulates pore
pressure profiles. 8) - Explains the
calibration of unloading limb stress/strain and demonstrates
that Hooke's law and fracture
pressure are limits. 9) - Organizes
and categorizes published empirical pore pressure methods.10)
- Points out some of the important ensuing applications
that are possible through synthesizing physical laws.
The Glossary – explains and relates over 100 technical
terms in earth mechanics.
Speaking broadly, chapter 1, 3 and 6 are [stress/strain]
conservation. Chapters 2 and 4 are [stress] conservation.
Chapter 7 demonstrates inter-dependant [load] conservation.
Chapter 8 explains how elastic and plastic mechanical
terms connect, both of which are conservation laws
in the earth. RETURN
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Physical laws combine in
the earth's sedimentary crust to explain all the above!
This
synthesis is a quantum step in the evolution
of geologic science, physical science, and civil engineering.
The synthesis applies to the common sedimentary minerals
from the surface to total consolidation. It applies
from 0 to 100% porosity with mineralogically
defined effective stress limits.
These
four panels shown above are central points of the earth's
mechanical system. They represent (UL) the effective
stress law in Normal Fault regime basins (chapter
4). (UR) Compactional and Hooke's law [stress/strain]
limits (Chapter 8). This [stress/strain] plane corresponds
to two sides of the [mass-energy]
limits
triangle. (LL) Fracture
pressure and hydrostatic limits to pore
pressure profiles (chapter 7). (LR)
Loading limb relationships for natural mixed-mineral
sedimentary rocks (chapter 3). All the above
are physically linked to each other in the earth's sedimentary
crust. The two right panels also appear on the cover
of "Deterministic Earth Mechanical Science".
The earth's mechanical limits
triangle describes the earth's [stress/strain]
limits using equivalent conservation laws. (Keep the
upper right [stress/strain]
diagram in mind if you jump to the limits
triangle now. The two triangles are mechanical
and conservation law equivalents.)
Minerals
and fluids
are the matter of our earth's mechanical system. Sediment
or rock composition reflects the sum of energy [effective
stress + fluid
pressure]. Loading and unloading
[stress/strain]
relationships are tangent to time sensitive [mass-energy]
conservation laws. Observations in the earth can add
new data points to the existing [mass-energy-space-time]
continuum.
Geologic and geophysical observables are consistent
with the conservation of [mass-energy].
We can use these observables interchangeably if we keep
in mind how they represent minerals and fluids. Reservoir
fluid and ground water production should trend along
a [mass-energy-space-time]
continuum.
The energy that drives continental
plates and reduces porosity is effective
stress. The sum of the
three vectorial principal stresses is conserved.
For plastic granular solids the compactional effect
of each vectorial stress is equal. There are three easily
recognized tectonic regimes in the earth's sedimentary
crust. Integer stress ratios that indicate vectorial-volumetric
stress equilibration dominate the observed data. These
are explained in chapter 4.
Effective stress minimization
explains how conserved vector and scalar energies
interacts in the earth. Porous grain
matrices respond by approaching a local
minimum effective stress state.
Stress equilibration can be through fault movement,
microscopic pressure solution, or both. Earth mechanics
explain earth physiography
and quantify the forces involved in continental drift.
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The
earth is a self-contained gravitational-mechanical system.
All
of the features on the map above are geometric. Tectonic
regimes and continental drift have previously been explained
only through relative stress relationships. Tectonic
regimes on all continents have been classified by observed
shear fault geometry. The three Andersonian fault regimes
have three corresponding shear fault orientations. Anderson
explained the relative but not
absolute magnitudes of the three principal
stresses. The additional concept of discrete energy
minima provides more closely quantitative
results and truly causal
explanations.
Shear faults and continental drift result from unequal
stresses. Gravity
is necessarily a principal stress in all three earth
tectonic regimes. Gravity
is either the maximum, intermediate or minimum principal
stress. Synthesis of physical laws provides quantitative
and balanced force predictions of the three principal
stresses.
There are three local
minima in the effective stress conservation.
The minima are integer relationships between the three
[v:H:h]
vectors within the average
effective stress scalar. The earth's
vectorial stresses are symmetrical about the integer
<2>.
Newton's gravitational law, Coulomb's electrostatic
law, and Einstein's theory of relativity also have physical
<2>
symmetry.
Data clustering about the positive integer ratio minima
is confirmed in normal and strike-slip tectonic regimes.
The
equations that limit earth mechanics are the extended
elastic equations of Hooke’s law and Newton’s
law. These operate in conjunction with other conservation
laws. Synthesis of these physical laws relates geologic
forces, grain-matrix-strain, pore
pressure and elastic wave propagation
directly to earth physical properties. These relationships
are co-dependant at the minimum [mass-energy]
equilibrium state. RETURN
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Mass-Energy
conservation within the earth
[mass-energy]
conservation within the earth is more complex than that
above the earth. But the earth's mechanical behavior
is readily understood through companion conservation
laws. Gravitational force varies in very close proportion
to overburden mass. It is directed
toward the earth's center.
The earth's reaction to gravitational force pushes out
against horizontal containment. The coupled minimum
horizontal load is exactly fracture
propagation pressure! It is a co-dependant
conservation law in accordance with [mass-energy] conservation.
Fracture propagation pressure
is a plastic, not an elastic relationship (as
explained in the earth's mechanical limits
triangle just below).
Newton's law and Hooke's law are linear parent
[mass-energy]
conservation laws. These two physical laws are vertices
of a new three-dimensional earth mechanics [stress/strain]
physical limits triangle. It is shown below.
Newton and Hooke's law [mass-energy]
conservation commonality was established well after
Hooke's death. The third vertex is the previously described
synthesis of physical laws that applies to the earth's
sedimentary crust. He's alive today and you can talk
to him. You can contact him by e-mail at phil@force-balanced.net
to place a book order or for more information. If you're
interested in the earth as a mechanical system, read
on. RETURN
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The
earth's mechanical limits triangle
The
details of [mass-energy]
conservation are explained in chapter 6 of Pore
pressure through Earth Mechanical Systems
"The article, Holbrook, P W, 2000, "How
do Poisson’s Ratio and Plasticity
relate to Fracture
Pressure?", World Oil , March,
pp. 91-96. briefly explains the [stress/strain]
triangle shown above. The left side of the mechanical
limits triangle is the lower half of figure 3 in the
article. Fracture Pressure
in the article is related to the left
side plastic
limit of the mechanical limits triangle,
not the right side elastic limit.
Hooke's law coefficients (i.e. Poisson's
ratio) have meaning only within the
elastic domain. Both limits
are explained and related in the article. This is a
.pdf file that will open automatically if an Adobe Acrobat
browser is on your computer system.)
The left side of the physical law limits
triangle corresponds to the lower half of figure 6.1
in the textbook and figure 3 in the article. The light
blue and tan
background areas translate
governing conservation laws into conventional mechanical
terms. Tan background
is [load-pressure-stress]
energy. The blue background area
is [mass-mineralogic
strain].
Quite naturally, [mass-energy]
conservation is three dimensional in our three dimensional
earth!
The [mass-energy]
plane is a matrix of conservation law equalities.
The [mass-energy]
equal (=)
signs are along the diagonal of the matrix. The solution
is a simultaneous summation of physical laws with connecting
conservation equations.
Even non-mathematicians appreciate the basic concept.
The whole is equal to the sum of its parts. In
this specific case, we are conserving [mass-energy],
which is the foundation of the physical science!
This summation raises [mass-energy]
conservation from one dimensional to three-dimensional
in our earth!!
Each of the equations on the plane is a physical or
conservation law. The vectors and scalars are conserved.
They are subscripted and color coded on the figure.
[Mass-energy]
are conserved from left to right and from top to bottom.
This is mathematically simple as are the final forms
of Newton's and Einstein's laws.
The right elastic limb of the mechanical
limits triangle
is the upper half of figure 3. This is the extended
elastic equations domain of Hooke's law. The Vp2 vs.
Vs2 planes shown on figures 1, and 2 are the elastic
mechanical systems plane. Figure 2 in the article
demonstrates that the dry and wet sedimentary clay minerals
have Poisson's ratio values of about 0.29. Water-wet
clay mineral have very low elastic moduli. Their associated
electrostatically bound water acts as a surrounding
cushion until almost all water is forced out due to
compaction.
Poisson's ratio is a constant for individual minerals
a virtual constant for SiAlic sedimentary clay minerals
at 0.29. Poisson's ratio as a mineralogic property does
not change with depth. Fracture
pressure changes in complete accordance with
[mass-energy]
conservation. This applies to clay, quartz, and calcite
minerals as well as mixtures thereof.
Minerals respond differently due to differing elastic
and plastic properties. Each mineral conserves [mass-energy]
with the means at it's disposal. Fracture
pressures in claystones, sandstones, and limestones
are different. But, they all respond in the same way.
This is an end-member plastic
relationship for all minerals.
The elastic mineral
and fluid
coefficients map directly from figure 1 to figure 3
in the article. Mass conservation
is identical in both domains. Thus we have both elastic
and plastic [mass-energy]
mapped on the same figure! Their representation as related
conservation laws was shown on mechanical limits triangle.
Earth mechanical limits are a direct response to [mass-energy]
conservation in the earth.
[Mass-energy]
is also conserved at the Newton and Hooke vertices of
mechanical limits
triangle. These two men are the founders of today's
mechanics. Pascal is the founder of fluid mechanics.
Isaac Newton, Coulomb and Hooke are honored by their
placement on the cover of "Pore
pressure through Earth Mechanical Systems".
I'm happy to have brought their physics together in
our host planet earth. RETURN
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Interior
of the Earth's mechanical systems triangle
Solid
matter response is asymmetrical within [mass-energy]
boundary conditions. The asymmetries are positive integer
ratios constant <2>
.Deep and strong rocks can store more potential energy
and "stick" longer. This stored potential
energy is released suddenly causing earthquakes. The
total energy released can be measured with seismometers.
The lowest earth [mass-energy]
occurs in recently deposited sediments that are just
below the earth's surface. These sediments have the
lowest strength and provide the truest direct measure
of [mass-energy]
in the earth. The even number tendencies prescribed
by the effective stress conservation law
are most closely met in these sediments. Physically
explicable deviations increase with increasing [mass-energy].
Data from the Long Beach Field is within the sheared
zone between the North American and Pacific plates (chapter
4). It shows strong [1:2:3] ratio predominance above
5000 feet. Data from the passive margin Gulf of Mexico
shows a strong [2:-1:-1] predominance. That even number
is also strongest in the shallow sediments. Stress ratios
in both sheared and passive margins, and in all lithologies
present seem to obey the effective stress
conservation law!
The mechanical systems triangle may be a curved surface.
The rates of relative particle motion increase from
the plastic to the elastic limits. Both limits are finite
and the shape of the triangle's surface can be mapped.
The triangle's surface is probably smooth and continuous
with respect to time, rate, mass and energy. A contoured
surface might provide a non-linear boundary to Newton's
law as Einstein's law did. Time and measurements will
tell.
The earth's interior is the only place where
humans can make such measurements. Geologists can examine
this unusually [high mass
low velocity] data. Whether near end-member data is
planar or curved bears on the overall [mass-energy-space-time]
continuum. Prediction of transitional time-dependent
[stress/strain] relationships will be more reliable
in either case. RETURN
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Why
learn about the
earth's two-phase mechanics?
The
earth is a two-phase planet. This earth specific
[mass-energy]
synthesis explains the forces
and fluid pressure
therein. There is no way of escaping the fact or this
conclusion. Most geoscientists must face and explain
earth mechanical relationships to other scientists and
engineers sometime in their career. Whether that explanation
makes mechanical sense or not reflects directly on us.
Other scientists can quickly detect mechanical nonsense
when they hear it. Anybody can tell when the dimensional
units don't correspond. If we are vague or speak
mechanical nonsense, our overall credibility goes down.
One possible short answer could be "Newton's law
applied under the earth's horizontal effective stress
boundary conditions." That definition when carried
out further goes on to explain force magnitudes in the
three earth tectonic regimes, continental drift and
compaction. These have been fundamental questions in
geologic sciences that have dozens of proposed answers.
All physically reasonable answers should be consistent
with the conservation of [mass-energy]
in the earth. This is an easy test to define that few
of the competing hypotheses can pass. Both the limiting
mechanical systems just mentioned conserve and relate
[mass-energy].
The transitional mechanical systems within the area
of the mechanical limits
triangle do as well. Stick along faults may be outside
the triangle for a geologic moment. But inevitably slip
or pressure solution will restore force balance.
Newton's [mass-energy]
answer applies above the earth. If you algebraically
add appropriate conservation laws, [mass-energy]
conservation works in the earth. It also explains a
whole lot about earth mechanics. [Mass-energy]
conservation in the earth represents significant forward
progress in the history of science and earth science.
Working professional geoscientists and earth science
students have a more pressing need to understand earth
mechanics. The pressures that we drill into can kill.
If you missed it, you can go back to the mass-energy
passage. Less dramatic but also very important is the
economic production of hydrocarbons from the earth.
Accurate continuous information about loads and fluid
pressures can be used to optimize hydrocarbon recovery.
See the paragraph immediately preceding the "why
learn"
question.
[Mass-energy]
conservation is accomplished by the earth throughout
production of a reservoir. [Mass-energy]
is neither gained nor lost. Most of our attempted force
fits to data are now done without using any boundary
conditions. Today's engineers and geoscientists are
generally unaware of the physically real constraints
that are expressed by the mechanical systems
limit triangle.
By not using real mechanical constraints, they
probably miss their fluid recovery objectives quite
often. Using mechanical constraints would give results
like a bowling lane with walls instead of gutters. Through
education we can first understand and then erect those
physically real mechanical systems limit
walls.
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The primary mission
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Other people with a general interest in physical science
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contains latest press releases. Related free_ publications
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