matter
field
multiply fractured rock region
oil reservoirs
account
shale gas
Coulomb's law
parameters
temperature track
rock region
nature
2015-07-01
boundary layer method
coupling
rate
hydrofracturing of boreholes
fluid extraction regime
drill mud permeation
mud
energy conservation law
basic regimes
electrodynamics
conservation laws
permeation
extraction regime
pressure
The invariant integral of physical mesomechanics as the foundation of mathematical physics: Some applications to cosmology, electrodynamics, mechanics and geophysics
terms
flow
Phe method
shape
cosmic fields
law
output
reservoir
cosmology
mud permeation
drill mud
false
geophysics
law of buoyancy
regime
variables
mathematical physics
article
203-212
foundation
fractured rock region
thermal energy
https://doi.org/10.1134/s1029959915030042
horizontal drilling
electromagnetic energy
track
fields of pressure
gravitation
continuum
charge
electric charge
fractures
gas
body
electricity
en
hydrofracturing
rocks
porous materials
equations
basic laws
Earth
region
general invariant integral
applications
mechanics
integrals
physical mesomechanics
method
dislocations
pressures of rock
Newton's law
2015-07
horizontal boreholes
Archimedes
2022-01-01T18:37
problem
diskshape fracture
mass
theory
mode crack
Phe physical mesomechanics
geometry parameters
boreholes
complex variables
materials
scale of nature
drilling
water
invariant integrals
binary continuum
fluid output
crust
energy
shale gas/oil reservoirs
scale
corresponding invariant integrals
fluid
notion
cracks
layer method
gas/oil reservoirs
fracturing
physics
functional equation
Phe general invariant integral based on the energy conservation law is introduced into physical mesomechanics, with taking into account the cosmic, gravitational, mass, elastic, thermal and electromagnetic energy of matter. Phe physical mesomechanics thus becomes a mega-mechanics embracing most of the scales of nature. Some basic laws following from the general invariant integral are indicated, including Coulomb’s law of electricity generalized for moving electric charges, Newton’s law of gravitation generalized for coupled gravitational/cosmic field, the Archimedes’ law of buoyancy generalized for bodies partially submerged in water, and others. Using the invariant integral the temperature track behind moving cracks and dislocations is found out, and the coupling of elastic and thermal energies is set up in fracturing and plastic flow, namely for opening mode cracks and edge dislocations. For porous materials saturated with a fluid or gas, the notion of binary continuum is used to introduce the corresponding invariant integrals. As applied to the horizontal drilling and hydrofracturing of boreholes in the Earth’ crust, the field of pressure and flow rate as well as the fluid output from both a horizontal borehole and a diskshape fracture issuing the borehole, are derived in the fluid extraction regime. A theory of fracking in shale gas/oil reservoirs is suggested for three basic regimes of the drill mud permeation into the multiply fractured rock region, with calculating the shape and volume of this region in terms of the geometry parameters and pressures of rock, drill mud and shale gas. Phe method of functional equations in the theory of a complex variable and the boundary layer method are also used to solve these problems.
articles
mesomechanics
Phe general invariant integral
volume
buoyancy
plastic flow
https://scigraph.springernature.com/explorer/license/
dimensions_id
pub.1036291333
1683-805X
Pleiades Publishing
Physical Mesomechanics
1029-9599
G. P.
Cherepanov
Resources Engineering and Extractive Metallurgy
18
The New York Academy of Sciences, 10007-2157, New York, USA
The New York Academy of Sciences, 10007-2157, New York, USA
Springer Nature - SN SciGraph project
Engineering
doi
10.1134/s1029959915030042
3