Thursday, December 27, 2007
Pressure and Stress in the Earth's Crust
Mammoth Creek, east of the Sierras, exhibits a N-S Anomaly, with Steam and active Faulting
Pressure and Stress in the Earth
All of you are familiar with the term pressure, since your faucet delivers water to you because of the pump pressure. Whenever the pump fails, or whenever too many neighbors use the water at the same time, you hear a gurgling noise from your faucet, and you phone the water company complaining of “Low Pressure”.
The use of the term stress may not be so recognizable, since it is used to connote bodily discomfort, how you feel in your auto on the freeway, or poor relations between family members. The usage of pressure and stress terms in the Earth’s Crust is defined below.
When you are lucky enough to drill a water well which has artesian flow, you have encountered a rare occurrence of fluid in rock- which is being squeezed by an Abnormal Force, causing water to flow out on the ground on its own impetus (no pumping necessary).
Both pressure and stress are defined by the force, F, exerted over an area a (either static or dynamic):
P, S = F/a, usually in pounds per square inch, psi, but also in dynes/square centimeter, or Newtons/square meter- in universal physical units. Notice that force or weight, not mass, is the entity measured.
The convention for Petrophysics or Rock Science is to categorize pressure as being a fluid measurement and stress as being a solid force exerted over an area of rock. These should be distinguished in three categories:
a. The fluid pressure is only exerted in the porous part of the rock (usually no more than 30% of the total volume), and it is exerted omni-directionally- that is, in all directions, since fluid works outwardly from a source without regard to direction. For Static conditions at equilibrium, this pressure is determined by the height of a column of fluid, e.g. .433 psi./foot x height for pure water (unheated and containing no minerals- one atmosphere is 14.7 psi or 33.95 feet of pure water, hence when water is put under a complete vacuum it will rise about 34 feet: 14.7psi/.433psi per foot = 33.95);
b. The solid stress is directional, and it is exerted on the rock frame, but may transmit itself to the fluid phase also, when the fluid cannot escape or relieve the pressure. Consequently, fluids in the earth may exhibit a pressure greater than that from a static column of fluid, and this may be:
S = density, ρ (Greek Rho or r), x gravitational constant g x height, or S.G. (specific gravity of rock, which is that density relative to water, as a ratio) x pounds/volume of water x height, or
S = S.G.(rock) x .433 psi./foot(water) x height of column of rock.
In the literature, you may see stress symbolized by σ (Greek sigma or s).
This last relation shows the stress exerted along the rock frame, which is transmitted to the fluid for the abnormal case. This again is a static stress, and is not the maximum stress which may be exerted on rock (the static overburden on rock is about 1 psi/foot thickness in sedimentary rock). Rock may temporarily exhibit stresses which are unstable, which are very large- sufficient to cause failure (earthquakes, sliding, or other movement). S.G. of rock is determined by its density, ρ = 2.65 for quartz x S.G of.433 for water = 1.15; clays are lighter:
S.G.(rock) = ρ(rock)/ρ(water) = density of rock(physics cgs or cm, gram, second units-
grams/cubic centimeter)/1.0, approximately.
An abnormally large rock stress usually results locally in faulting or slumping and creep, but if unrelieved completely may be observed directionally along fractures (jointing as indicated by geological terminology). It is usually very difficult or impossible to determine the original magnitude or rate of relief of stress, but the orientation easily may be seen in fractures or fault movement. A clue to regional stress on rock is noted by parallel fracture lines in flat rock, and these may occur consistently over hundreds of kilometers.
c. The stable column of rock may contain two stress indications:
i. the pressure on the fluid phase P = S.G. of water x .433psi/ft x height;
whereas the rock stress:
ii. S = S.G. of rock x .433 x height of rock, psi. S.G. of rock is at least 2.5 (gypsum is an exception, with 2.3) and normally S is approximately 1.0 psi/ft. At 10,000 feet, normal water head is 4330 psi, whereas it may be confined in rock with normal overburden at 10,000 psi. But
iii. S > greater than S(static rock) may accompany water at normal hydraulic head, whenever there is an active solid stress such as in volcanic areas (with water unconfined). The > symbol connotes greater than, with < meaning less than.
Hot Springs near Tofino, Vancouver Island, Canada exit on a peninsula near the Pacific Ocean
This all sounds strange, but consider your auto windshield- which may have free-flowing water rolling down its flat surface, while the solid glass is under extreme stress from its curved configuration.
Now consider these other rare occurrences:
1. A lens of sediment, surrounded by impermeable shale or clay, contains water with no possibility of quick escape. Whenever this lens is squeezed by the overburden or other force- either lateral or vertical- the water will carry the total stress of the confinement, which may be about 1 psi/foot (double the normal hydraulic head expected). This yields a blowout in an open or water-filled drill hole, whenever the lens is drilled (since the water now has an exit- right into the borehole). Oil Drillers are aware of this case, and it is overcome by putting high density materials in the drilling mud.
2. An isolated lens of rock may have sufficiently high temperature, such that Methane or CO2 gas is being generated faster than it can exit the lens. This is a fairly normal case in the deep earth, (greater than 5 kilometers depth), since there is high temperature everywhere. This is abnormally-high pressure, named Geopressure. Even in intrusive rock, such as granite, there is sufficient bacterial and organic activity to generate gas release. An interesting case occurring at this writing is located in East Java (near Surabaya), where a driller for oil encountered high pressured hot shale which has been flowing over several square miles for many months without stopping. The mud has flooded many houses.
3. The strangest case, which I have investigated- publishing a professional paper about it- is that of under-pressure. This occurs whenever there is CO2 baked out of deep limestone- by a hot intrusion- which remains in the gaseous phase, and when the gas percolating upward encounters fresh water not saturated in the carbon-dioxide. In this case, the gas quickly dissolves in the fresh shallow water and the volume of gas plus water shrinks- reducing the pressure when the permeability is abnormally low. For the Rocky Mountain area, this is not too rare, and the borehole fluid may be sucked into the permeable zones containing under-pressured fluid (P< .433psi/ft x depth). Pressure at 10,000 feet depth is less than 4330 psi, for this case.
4. Even in normally-pressured areas, where the water table is deep (as near the Grand Canyon), the pressure at the bottom of a drilled hole will be much less than .433 psi/foot x depth, since most of the borehole is filled with air or light weight fluid. In this case,
P= .433 psi/foot x height of water in the well bore, from water table to bottom hole. This is normal pressure with abnormal depth of water, since the water has drained out into the canyon. This will occur on mountains also where the water has percolated toward springs near the base of the terrain. In the western USA, it is common in the desert for the water table to occur many feet below the ground surface, where water pressure is normal wherever it is found. Only in abnormally hot or stressed rock will there be abnormal water pressure. The stress may derive from tectonics, from movement along faulting, and from generation of gas from organics abnormally heated.
Summing all of this, the pressure of the fluid in the Crust is unknown until it is measured. It can be estimated from gradients measured in nearby wells, or taken to be the normal pressure dependent upon the depth where it is found, but it is never known precisely until it is measured. The main reason for this uncertainty is that the Earth stress generating the pressure other than normal is unknown and cannot be determined in advance. This further illustrates the dilemma for Geologists, that since they never know with certainty what lies below their feet, they cannot know what the stresses will be there either.
How one can overcome this dilemma is to make regional maps and isolate the areas which are anomalous in some property which can be determined in advance- for example, gravity, temperature, acoustics, or spontaneous potentials (resulting in terrestrial, sometimes named Telluric, currents) in the earth. Anomalous geological, geothermal, or geochemical areas can be expected to exhibit anomalous stresses and pressures.
Location of Anomalous areas, by use of Geochemical Maps
I have mapped properties obtained from well logs and springs over regions as large as a county. The physical parameters which may be found from well log libraries and water chemistry may be plotted on a map- regardless of the uncertainty of depth of origin. These include;
1. Spring and wellbore temperatures;
2. Spring and well logged water salinity concentrations, TDS or total dissolved solids:
3. Formation Resistivities and Spontaneous Potentials (SP);
4. Radioactivity Magnitudes and individual elements’ gamma ray magnitudes;
5. Temperature Gradients, or temperature change from ground surface to bottom hole depths, Gt = Tbh –Tsurf/Depth, in hundreds of feet (This number will generally be 1.0 degrees/hundred feet, F change/hft or larger). This is better than using T alone, since temperature regularly increases with depth in the earth, and gradients can be compared from well to well. However, springs temperatures have no depth and must be used directly. The temperature of springs does vary with elevation in the mountains, and with latitude, so that one must compare T with others in a given latitude and elevation. A graph may be made at any latitude, showing the variation with elevation, and an extrapolation for the elevation of interest is simple. The normal temperature is near the annual mean temperature of the shallow subsurface (100 feet deep);
6. Concentration of any ion of interest must be normalized for evaporation or concentration caused by handling- the most trusted anion is Cl¯ , which does not interact with other ions or solids significantly (Cl ion has a half life of millions of years), and it is used in the following way:
K(normalized) = K+/Cl¯, using similar units for both ions; and,
7. Soundings of resistivity variation with depth, to locate Water Tables (lowest resistivity) or Rock with unusually high resistivity.
When a map is made on any one of the above parameters, any anomalous magnitude will stand out- showing that it is significantly different than the trend. This allows it to be inspected on its own merits, so that it may be confirmed as being anomalous. An example is that for SP, which varies with water salinity, water movement (Electro-kinetic Potential), and chemical oxidation-reduction (Redox) reactions. A map made on this parameter, countywide, will show sudden changes, which indicate either moving water, unusual chemical activity (such as reactions involving Uranium, Sulfur, or noxious gases), or strong brines (which are associated with oil, evaporites, or salt domes). Other means must be used to determine which of several possibilities are involved, but the anomaly is definitely located using this process.
Mammoth lake, CA has many indications of active movement of the Crust, including Steam, Water, Vulcanism, and Fissures