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OCR for page 158
160
Constant pressure/ Initial Conditions
temperature boundary
Temperature,°C
100 200 300 400
\\
\ \T(40 ° C/km)
P(S atic) \ \
v 500 1000
C O2 Pressure, bars
Controlled flux boundary
3.17 x 1 0 ~3kg/s CO2
(plus 85 mW/m2)
FIGURE 1 1.1 Schematic diagram of the one-dimensional model
used to simulate CO2 movement through the crust. Graph shows
initial temperature and pressure profiles. The CO2 flux at the
lower boundary is derived by assuming that the global flux of
CO2 (about 3 x 10~2 moles per year) is distributed over 1 percent
of the Earth's surface area (1.3 x 106 imp. The heat flow is
typical of tectonically active areas.
heat by solving the appropriate set of coupled partial dif-
ferential equations. It was originally developed to simu-
late geothermal reservoirs (Bodvarsson, 1982~; we modi-
fied it to describe the properties of CO2 rather than H2O.
In our particular case we assumed one-dimensional flow
vertically upward through a prism of crust, and we specify
at the bottom of the prism what we believe to be a reason-
able flux of CO2 and heat. We then adjusted the permea-
bility in the course of a set of numerical experiments. A
schematic diagram of the model is shown in Figure 11.1.
For the purposes of calculation we assumed that the pore
fluid is pure CO2. The fluid properties of CO2 were ob-
tained from Kennedy and Holser (1966), Jacobs and Ker-
rick (1981), Vargaftik (1975), and Atkins (1978~. The
published density and viscosity data had to be extrapolated
to higher pressures. Over the pressure and temperature
ranges considered, CO2 appears to have transport proper-
ties that are quite similar to water (Figure 11.2~.
We assumed as the lower boundary condition a con-
stant influx of CO2 and heat. One can hypothesize other
conditions at this lower boundary; however, for an initial
calculation, constant flux provides insight. We have taken
the flux as 3 x 10~2 moles of CO2 per year, which seems
well within the estimates given in Table 11.2. This flux is
distributed over the tectonically active area, which we
have taken as 1 percent of the Earth's surface; it is then
something of an average and may be substantially higher
or lower locally.
JOHN D. BREDEHOEFT AND STEVEN E. INGEBRITSEN
Given this set of simple assumptions, we made a series
of calculations to determine how low permeability would
have to be in order to cause pore pressures approaching
lithostatic conditions by simple permeation (i.e., without
invoking enhanced transport or focusing effects). The results
are summarized in Table 11.3. Since the model is run in a
transient mode, the results are presented in terms of the
time to reach lithostatic fluid pressure at 10 km depth, the
lowermost cell of our simulated column of crust. At a
permeability of 10-7 darcies, pore pressures do not ap-
proach lithostatic at steady state (infinite time). Given our
assumed flux, the permeability must be on the order of
10-8 darcies or lower to generate pore pressures near
lithostatic. Figure 11.3 shows pressure profiles at venous
times as the pressure builds to lithostatic for a case in
which pe~meability is 10-9 darcies. In Figures 11.3 through
11.6, k is permeability, Cr is rock compressibility, and o is
porosity. Typical ranges of rock permeability are given by
Brace (1980) and are discussed below (see Figures 11.7
and 11.8~.
-- CO
___ H2O
°r
Density (g/cm3)
1 1 1 1
Viscosity (poise x 10-3
1 1
2500 L--
0200 400
Temperature, °C
FIGURE 11.2 Density and viscosity of CO2 and H2O as func-
tions of pressure and temperature. CO2 properties (bold con-
tours) are dashed where extrapolated from published data. H2O
properties are from 13urnham et al. (1969), Keenan et al. (1969),
and Haar et al. (1984). The pressure-temperature range of our
experiment is shown by shading.
OCR for page 159
SOURCE OF HIGH PORE PRESSURES IN THE CRUST
TABLE 11.2 Global Carbon Reservoir (from 5
Sundquist, 1985)
Reservoir Carbon (10~5 tonnes) 6
Atmosphere 0.036
6.4
7.3
Oceans
Continents
Carbonate rocks
Oceans
Continents
Metamorphic rocks 10
28
54
Total 106
TABLE 11.3. Time to Reach Lithostatic
Pressure at a Depth of 10 km
Permeability
(darcy)
10-8
Porosity
10-9 0.01
0.02
0.01
0.02
HYDRAULIC FRACTURING
Time (106 yr)
0.15
0.30
1.5
3.0
If the boundary condition at the base of a rock column
of low permeability has a constant influx of CO2, it is
possible to calculate arbitrarily high pore pressures. At
some point increased fluid pressure will generate either a
hydraulic fracture or a shear failure, which would increase
the local permeability. The nature of the failure depends
~ .
9 _
Initial
pressure
k = 10-9 darcy
C,= 10~5bar
.. ~ = 0.01 -
·-...
.. Li~ostatic ~
pressure
it\\
to\\ \ Time,
~ ~1 coo s years - . _
10 ~1 lo TO ~60 100_~134-_=
0 500 1 000 1500
Pressure, bars
2000 2500
FIGURE 11.3 Pressure-depth profiles for venous times after
initiating flux of CO2 into bottom of column (see Figure 11.4~.
161
9 _
~-. k= 10~9darcy
_ \ . C, = 10-5 bar
lo\ .. ~ = 0.01
t ~1000's Years .
Initial ~
pressure |
1 ~' ---- ~ ~ ~ ', .
2000 2500
10, ' 500 1000 1500
Pressure, bars
FIGURE 11.4 Pressure-depth profiles for venous times. Once
lithostatic pressure is reached, permeability is increased 1000
times, simulating the effect of fracturing.
on the local state of stress. In the case of a hydraulic
fracture, a true tensional opening, the fracture will occur
normal to the least principal stress. The fracture will occur
when the pore pressure exceeds the sum of the least prin-
cipal stress and the tensile stress of the rick. If the least
principal stress is horizontal, the hydraulic fracture will
tend to be a vertical opening. A variety of fracture orien-
tations are possible depending on whether they represent
shear or tensional openings and the local state of stress.
When the vertical permeability is increased locally, pres-
sure effects are distributed upward very quickly. The
lithospheric load is a convenient upper bound for failure.
We have attempted to simulate a system in which hy-
draulic fractures are created. It seems that two possible
processes can occur following fracturing. Once the pres-
sure falls following the break, the fissure can (1) remain
open, thereby increasing the local permeability or (2) seal
itself, and return to something approaching its initial per-
meability. We have attempted to simulate both occur-
rences.
Figure 11.4 illustrates the pressure history in the lower
portion of the column in the case where the fracture per-
meability remains high following a break. In this case
permeability is increased 1000 times once the pressure
within the simulated rock block reaches lithostatic. Note
that lithostatic pore pressure migrates upward with time
and that once breaks occur in the lower rock units they do
not reach lithostatic pressures again. Figures 11.5 and
11.6 show what happens when the breaks are resealed, that
is, permeability is returned to its original value following
a break. The pressure once again builds to a lithostatic
level at the bottom of the column, a second break occurs,
and this sequence continues to repeat itself. As in the case
OCR for page 160
162
5
6
9 _
10< ~
:. k = 10-9 darcy
Immediately C r = 104bar
before fracturing . ~ = 0.02
Immediately '..
after fracturing
. Lithostatic
~ pressure
Time,
~ OOO's years ..
pressure ~ ~
500 i 1000 1500 2000 2 00
Pressure, bars
FIGURE 11.5 Pressure-depth profiles for venous times for a
system in which fracturing occurs once pressure reaches lithostatic
and fractures quickly reseal themselves. In the simulation the
following sequence is followed: (1) once pressure reaches
lithostatic, permeability is temporarily increased 1000 times; (2)
pressure drops quickly; and (3) once pressure drops, penneabil-
ity is set back to its initial value, and the cycle repeats itself.
There are two sets of profiles: the solid profiles are immediately
before the fracturing and the dashed profiles immediately after.
ce
Pressure increases consistently with time within each set.
JOHN D. BREDEHOEFT AND STEVEN E. INGEBRITSEN
ing are also suggested by studies of hydrothermal ore
deposits (see Titley, Chapter 3, this volume).
DISCUSSION
The results of our analysis suggest that degassing of
CO2 could be a source of high pore pressure, provided that
the permeability of the rocks is sufficiently low. We must
now consider whether such low permeabilities might rea-
sonably be expected deep within the crust.
Brace (1980) has compiled both laboratory and field-
measured permeability values for crystalline and argil-
laceous rocks. Figures 11.7 and 11.8 are adapted from
Brace. Clearly, the values suggested by our simulation are
in the lower range of what has been measured, both in the
laboratory and in situ. If one examines only the in situ
4
2
o
-2
4
-6
Laboratory Permeability
t
Sand
I Sandstone
Limestone
Volcanics dolomite
Meta
| Siltstone Gran jte ~ orphics
| Ihaie l l l
where the fissure remains open, the breaking will migrate
upward (Figure 11.6~. An interesting feature of this model
is the pulsing nature of the pore pressure at a given depth
(see Figures 11.5 and 11.6) Gold and Soter (1985) sug
gested a similar mechanism in considering the migration
of fluids through the crust. Repeated episodes of fractur- FIGURE 11.7 Range of laboratory permeabilities for different
rock types (from Brace, 1980~.
2S0or l ~A. ~. ~I !
2000
1 000
I
.
500 t 1
/ / V . Lithostatic
/ / .. ~pressure
D / Depth, km
~ 1500 / 9 5
~ /..
.
~ '. :
1 1
1 2
Time, 1 OO,OOO's years
k = 10-9 darcy
or = 10-4 bar
=0.02
3 4
FIGURE 11.6 Pressure versus time for a system in which frac-
tunng occurs once pressure reaches lithostatic and fractures
quickly reseal themselves.
-8
-10
-12
Gneiss
values, they are very near the low end of what has been
measured. However, most of the in situ values have been
measured near the Earth's surface, usually at depths above
500 m. It is our judgment that rock permeabilities in the
range of 10-8 to 10-9 darcies are low but within the realm of
expectation deep within the crust.
We have assumed in our calculations that the pore fluid
is entirely CO2. There is likely to be some H2O present in
the crust in the pressure-temperature range of the experi-
ments. If significant amounts of both H2O and CO2 are
present, the pore fluid would be a homogeneous single-
phase mixture of H2O and CO2 at temperatures 2300°C
and a heterogenous two-phase mixture of H2O-rich liquid
and CO2-rich vapor at lower temperatures. The presence
of NaC1 or other electrolytes would extend the two-phase
region to higher temperatures (Bowers and Helgeson, 1983~.
OCR for page 161
SOURCE OF HIGH PORE PRESSURES lN THE CRUST
4
2
o
-2
o
-4
-6
-8
-10
-12
In Situ Permeability
'1~' 1' l,...
Gig ; Gig I I - I i S cCD to I I
_ c ~ . 0 co
a, _
cO cn
or
Crystalline
JO
Argillaceous
FIGURE 11.8 Range of in situ permeability measurements for
crystalline and argillaceous rocks from various sites around the
world (from Brace, 1980~.
The limited solubility of CO2 in H2O in the pressure-
temperature range considered (Takenouchi and Kennedy,
1964; Gehrig, 1980) implies that the volumetric flow rate
required to transport a given flux of CO2 in solution or in
a two-phase mixture would generally be somewhat greater
than the flow rate required to transport the same CO2 as a
separate phase. Since the density and viscosity of H2O and
CO2 are comparable (Figure 11.2), the limiting permea-
bilities suggested here for anhydrous systems may be rea-
sonably limiting values for hydrous systems as well.
Chemical controls on the buildup of CO2 pressure may
significantly constrain the applicability of our analyses.
CO2 pressures in natural systems at temperatures of 200°
to 400°C will generally be limited by the reaction of Ca-
Al-silicates, H2O, and CO2 to form calcite and mica and/or
clay. At 300°C, for example, the partial pressure of CO2 is
likely to be on the order of tens of bars (Giggenbach,
1986~. Where the available feldspar is converted to calcite
and mica and/or clay, or the supply of H2O is limited, the
partial pressure of CO2 is not fixed and may increase to
greater values. This might occur where the flux of CO2 is
greatest (e.g., in fault zones and volcanic terranes). In
general, CO2 flux may be lower and/or permeabilities higher
than those required to create high pore pressures; other-
wise, we would expect most Ca-Al-silicates in the upper
crust to be altered to calcite.
i63
The question of fluid movement and pore pressure within
the deep crust is complex. The intent of this chapter was a
simple bounding calculation; we hope that it will provoke
further thought, debate, and analysis. On balance it seems
possible that fluid CO2 migrating through the crust may
yield high pore pressure where the rocks deep in the crust
are sufficiently "tight" and the local geochemistry does
not preclude high CO2 fluid pressures.
ACKNOWLEDGMENTS
We thank R. O. Fourier and H. R. Shaw for helpful
reviews of this manuscnpt. Our brief discussion of chemi
cal controls on CO2 pressure is based largely on Fournier's
comments.
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Baes, C. F., H. E. Goeller, J. S. Olsen, and R. M. Rotty (1976~.
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Des Marais, D. (1985~. Carbon exchange between the mantle
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Gehrig, M. (1980~. Phasenglichgewichte und PVT-daten ter-
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Freiburg, Germany.
Gerlach, T. M. (1986~. Carbon and sulphur isotopic composition
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Gerlach, T. M. (1988~. Plutonic degassing of carbon dioxide at
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Gold, T., and S. Soter (1980~. The deep-Earth-gas hypothesis,
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Hubbert, M. K., and W. W. Rubey (1959~. Role of fluid pressure
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Jacobs, G. K., and D. M. Kerr~ck (1981~. APL and Fortran
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Steam Tables, John Wiley & Sons, New York.
Kennedy, G. C., and W. T. Holser (1966~. Pressure-volume
JOHN D. BREDEHOEFT AND STEVEN E. INGEBRITSEN
temperature and phase relations of water and carbon dioxide,
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97, Geological Society of America, Boulder, Colo., pp. 371-
383.
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OCR for page 163
Index
A
Actinolite, 82
Advection, 9, 29-30, 31, 32, 33, 47-48
Africa, 132, 145
Alaska, 81, 137, 148-155
Alberta, 136, 137
Alps, 10, 32, 69, 153
Aluminum
andalusite, 98, 101, 109
chlorites, 77-78, 82, 83, 98, 99
mica, 97, 98, 99, 100, 106, 163
see also Feldspar
Amphiboles, 82, 88, 97, 98-99, 101, 106,
109, 153
Anatexis, 108-111
Andalusite, 98, 101, 109
Appalachian Mountains, 12, 35, 132, 133,
134-135, 136, 138, 140-146, 153
Aquifers, see Groundwater tables
Arizona, 38, 51, 52, 54, 55, 58, 130
Arrow Lake, 78
Asia, 145, 158
see also geographical subunits
Atlantic Ocean, 150
B
Barbados, 150, 153
Barium, 15
Basalts
carbon dioxide solubility, 159
fluid-rock ratios, 65
magma, 84-90, 159
Basement complexes
Hercynian orogeny, 98, 99, 100, 103,
106-110
seismic reflection, 128-138
Batholiths, 33, 54, 75-80, 81, 87-88, 115
Bentonite, 33
Biotites, 77, 82, 99, 101, 103, 104, 105
Boreholes, see Drilling
Boundary conditions, 15, 16, 23
Breccias, 53, 80
Brines, 20, 125, 133-138
British Columbia, 73, 81
cordilleran batholiths, 75-78
British Institutions Reflection Profiling
Syndicate, 128
Brittleness, 5, 54, 73, 90, 111, 116
C
Calderas, 79-80, 81, 84-85, 89, 90
California, 21, 22, 81, 136
San Andreas Fault, 12-13, 35-36, 116
Canada, 135, 136, 137
see also geographic subunits
Carbonates, 64-65, 68, 98-105' 106, 109, 158
Carbon dioxide, 5, 39, 64, 65-66, 96, 130,
141, 154, 159-163
Carboniferous period, 97, 98, 99, 105, 106,
109
Carbon isotopes, 96, 158-159
Cascade Mountains, 80
165
Caspian Basin, 14, 36, 37
Cenozoic era, 51, 76, 84
see also Quaternary period; Tertiary period
Channelized flows, 9, 29, 45, 47-48, 69-70,
132
Chemical processes, 4, 5, 8, 9, 19
carbon dioxide, 5, 39, 64, 65-66, 96, 130,
141, 154, 159-163
diagenesis, 12, 13-15, 27, 36-37, 134, 149
equations, 4, 10, 31-32
fault zones, 153
free water, 5
global geochemical budget, 149
hydration/dehydration, 15-16, 37-38,
56-57, 68
metamorphism, 64-65
phase equilibria, 4, 64, 65, 66
quartz precipitation, 69-70
research recommendations, 21
salt and systems, 20, 59, 65, 133-135
transport, 3, 31-33, 48
volatiles, 39, 47, 67-6S, 69, 132, 158
see also Isotope geochemistry; Minerals
and mineralogy
Chlorites, 77-78, 82, 83, 98, 99
Clay, 11, 14, 37, 67, 82, 150
bentonite, 33
montmorillonite-illite transformation, 14,
17, 37'39, 134, 149
petite, 65, 68-70, 98-99, 100, 101, 102,
107, 108, 111
Coal, 133
Colorado, 22, 33, 81, 90
OCR for page 164
166
Computer applications, 4, 22
fracture processes, 19, 20
heat/mass transport, 15
Conservation equations, 6-9, 28-32
Consortium for Continental Reflection
Profiling, 128-138
Contamination, 10, 21, 27, 31-32
Continental margins, 64, 75-76, 132, 138
Convection, 6, 15-16, 27, 30, 33, 37, 38, 42,
50, 73, 77, 90, 110, 111
Cordilleran phenomena
batholiths, British Columbia, 75-78
hydrocarbons, 136
Cores, see Drilling
Coupling of processes, 3, 10, 14, 17, 22-23,
32, 38, 39, 48, 153, 160
Cretaceous period
meteoric hydrothermal activity, 76, 81
shale, 8, 33, 96
Crystalline rock and crystallization, 8, 19, 38
basement complexes, 98-100, 103, 106,
107, 108, 109, 110, 128-138
batholiths, 33, 54, 75-80, 81, 87-88, 115
chlorites, 77-78, 82, 83, 98, 99
geometry, 84
granitic, 97
magmatic, 16, 38, 45, 46, 47, 53-54, 80,
83-84, 87, 9~91
paragenesis, 55-59
permeability/porosity, 8, 47, 83-84
pressure relations, 117
see also Quartz
D
Darcy's Law, 7, 10, 28-29, 30, 32, 34, 37,
150 F
Deep crustal processes, 4, 5, 16-17, 38, 64,
96, 128-138
Density, 10, 15, 29, 32, 37-38
fracturing, 58, 59
pressure and, 38, 43, 68, 82
rock/mineral, 43, 68
Devonian period, 35, 97, 135, 141, 143-144
Diagenesis, 12, 13-15, 27, 36-37, 134, 149
Differential equations, see Equations
Diffusion, 15, 29-31, 32, 117
see also Advection; Convection
Dispersion processes, 29-30, 32
Drilling, 5, 58, 86, 90, 96, 111
Ductility, 5, 89, 90, 111
E
INDEX
Energy factors, 47
Energy resources
coal, 133
hydrothermal, commercial use, 16, 38
natural gas, 21, 27
oil, 10, 21, 27, 135, 136
Energy transport, 3, 6-7, 27-32, 30
see also Heat transport; Momentum
Eocene epoch, 78
magmatism, hydrothermal effects, 78-80
Epidote, 82, 83
Equations, 3
boundary conditions, 15, 16, 23
carbon dioxide flux, 159-160
conservation, 4, 6-9, 28-32
coupling of processes, 3, 10, 14, 17,
22-23, 32, 38, 39$ 48, 153, 160
Darcy's Law, 7, 10, 28-29, 30, 32, 34, 37,
150
density, 37-38, 68
dispersion-diffusion-advection, 29-30, 31,
32, 33, 48
geothermal reservoirs, 16, 38
hydration/dehydration, 38-39
magma-associated flow, 38, 42
permeability, 60, 120
pressure effects, 4, 10, 29, 32, 37, 42-48,
68-69, 120, 121, 122
research recommendations, 22-23
stress and strain, 31, 36-37
tectonic stress, 35, 121
time factors, 121-122
volume, failure, 46-47, 48, 122, 123
Europe, 106, 158
see also geographical subunits
Earthquakes, 3, 5, 10, 21-22, 27, 33, 115,
124
Elasticity, 30, 45, 124
visco, 22, 32
see also Stress and strain
Electrical conductivity/resistivity, 5, 11, 33,
115, 150
Electromagnetic techniques, 5, 115
Elkhorn Mountains, 81
Faults, 149, 150, 151-154
Appalachian Fold-Thrust Belt, 35, 140-146
joint/fracture systems, 54, 144-145, 146
magma conduits, 129
rift zones, 72, 86, 87, 89, 90, 91, 109, 110,
129-130
San Andreas, 12-13, 35-36, 116
strain rates, 121, 124
see also Earthquakes
Feldspar, 73-75, 78, 81, 82, 83, 88, 99, 101,
104, 134, 163
plagioclase, 82, 83
sericite, 83, 98
see also Granite and granitoids
Fick's Law, 29
Field studies, 17-19, 33
fluid inclusion, 150-155, 158
joint sets and systems, 51-61, 144-145,
146
Finger Lakes, 141
Flows
artesian, 141
channelized flows, 9, 29, 45, 47-48,
69-70, 132
flow equations, 29
grain boundaries, 8, 65, 69
lithostatic fluid pressure, 5, 10, 14, 21, 33,
37,66,67-69,90,91, 110, 111, 117,
12~123, 141, 145, 146, 149-151, 158,
159
mid- to lower-crustal levels, 5, 16-17, 64,
66-68
velocity, 20, 28, 29, 68-69
viscosity, 10, 22, 37, 46, 47, 66, 68-69, 82,
120
see also Advection; Convection; Diffusion;
Permeability and porosity
Flux, 9, 30, 31, 6066, 68-69
carbon dioxide, 159, 160, 163
Darcy's Law, 7, 10, 28-29, 30, 32, 34, 37,
150
mass/energy, 6-7
thermal, 44
Fourier's Law, 30
Fracture processes
brittleness, 5, 54, 73, 90, 111, 116
channelized flows, 9, 29, 45, 47-48,
69-70, 132
deep crustal, 5
diffusive, 29
failure criteria, 15, 27, 38, 44, 45-48, 50,
54, 122, 123, 124
gabbros, 84
healing/sealing, 118, 120-121, 122, 124,
151
hydraulic, 6, 8, 13~16, 27-28, 36' 38, 42,
45, 54, 68, 69, 117-120, 122, 123, 144,
150, 151-152, 161-162
hydrothermal, 5~61, 69
joint sets and systems, 50-61, 144 145,
146
magma, 44-48, 50-61
mineralization, 4, 15, 27-28, 47-48, 53,
55-59, 69-70, 81, 82, 118, 12~121,
122, 124, 153
ocean lithosphere, 123
permeability, 6, 20-21, 27, 5~61, 78, 84,
90
research recommendations, 17, 19
France, Pyrenees, 33, 65, 73, 89, 91, 96-111
G
Gabbros, 73, 81-84
Geometry
crystallization, 84
fractures, 19
joint/fracture systems, 51, 54-59
pores, 42, 45
Gold, 81
Gneisses, 97, 98-99, 101-110 (passim), 117
Gondwanaland, 137
Grain boundaries, 8, 65, 69, 118, 149
Granite and granitoids, 73, 76, 77, 98, 99,
100, 102, 105, 108
crystallization, 97
gabbros vs. 73, 83-84
gneisses, 101
Representative terms from entire chapter:
pore pressure
