Comparison of Technologies which intend to dilate the rock to
Propellant and Common Explosives Techniques

Propellants and Gun Powders

During the burning process (deflagration) of solid propellants or gun powders build-up pressure of generated gas (which is the main force for cracking in such technologies) does not exceed 10,500 Psi per second. Unconfirmed reports from competitors claim to generate, as much as, 20,000 Psi.

Figure 1.  Change of generated pressure P  in time, during burning of propellants and gun powders (deflagration) under hydrostatic stress P_s, where initial amplitude P_m does not exceed 50 MPa. Impulse duration reaches 2 seconds.

Because gas pressure is growing with such slow speed usually no more than 2 of vertical fractures are created. According to Lame’, the wave, attenuation is inversely proportional to the square of the distance from the cylindrical charge () and to the cube of the distance from the shaped () charge:

  and  

Where:
- wave attenuation
- initial pressure created by the products of burning or detonation process
- the distance from the center of charge to the point where maximum principal stress was measured

Bedrocks vary in strength and gas will find weak points where cracking begins under advanced conditions. As propagation of initial fractures progress, gas will be consumed faster than propellants can generate it. As a result no new fractures can be created. Gas consumption will continue until pressures decrease to a certain level at which fracture growth stops. This process is explained by the law of  A. Griffith:

Where:
- uniaxial tensile strength of the rock
- the free surface energy per unit area
- a Young’s modulus
- the length of a fracture propagated in one direction

Click on this link to check references: Microcracks and Shear Fracturing

Common Explosives

The detonation of common explosives create an impulse or wave that attenuate according to the law

  and  

Where:
,  and - experimental factors
- maximum principal stress
- an arbitrary distance from the center of the charge to the point where the maximum principal stress was measured
- mass of the charge
- index of the symmetry of explosion

Figure 2.  Stress state of the rock created by the detonation of the shaped charge (Common explosive methods)

Line 1  -
Line 2  -
Line 3  -

Where:
- maximum principal stress
- amplitude value of radial component
- minimum principle stress
- time as a part of the total wave duration
- differential stress

From Figure 2 we can see the value of varies from 0.34 to 0.58 with an average value of 0.4. This is slightly higher than its value under effective normal stress.  Semi-analytic expression for the shear-stress relaxation modulus is:

Where:
- Poisson’s ratio.

Therefore, reaches parameters when the main deformation force is the force of compression. This residual stress of common explosives can actually reduce permeability of the rock near wellbore.

Figure 3.  Volumetric deformation of the sandstone with its strength from 85.5 to 106 MPa

Where:
   Line 1 - compressive deformation with value = 1common explosives
   Line 2 - compressive deformation with value = 0.165common explosives
   Line 3 - beginning of dilation with value = -0.05common explosives
   Line 4 - dilatant deformation with value = -2.35SWTorpedo
   Line 5 - dilatant deformation with value = -1.25SWTorpedo

In Figure 3 we can observe compressive deformation and its decline. The decline of compressive deformation and increase in rock volume is due to the decreasing of value of .

Quotation:
Rock fracture in shear depends on microcrack propagation where the propagation is caused by tensile stresses. Where are the tensile stresses generated when rock is deep within the crust of the earth? The answer is that on a microscopic scale grains press against each other at sharp contacts. These contacts are called "stress risers". Under these microscopic contacts very large tensile stresses can be generated even though the whole-rock stress in highly compressive.

Click on this link to check references: Chapter 9 Mechanics of Fracturing and Faulting

Only dilatant technology will justify commercial applications of high explosives to deliver cost-effective increase in well productivity by increasing permeability 200% or more.

Dilatant Increase of Rock Permeability Using High Explosives

Laboratory and field experiments confirm that dilatancy begins when ( ζ = σ_φ/σ_r ) < 0.1 will progress when the value of ζ  approaches  -0.1 and will reach its peak when ζ  value is negative 1.0 in the areas where: σ_r  at its amplitude and the amplitude is not lower then 3% of the rock’s uniaxial compressive strength.

Figure 4.  Distinctive characteristics of the dilatant stress state created by SWTorpedo during its detonation.

In Figure 4 displayed registered tensile stress and rock fracturing in shear when 2 staged SWTorpedo with cumulative TNT amount of 8lb was used. Dash line shows the how θ (volumetric deformation) is vary with change in ζ  value. During detonation of SWTorpedo compressive volumetric deformation appears only in the initial stage of wave’s propagation when maximum principal stress as low as 17.5MPa or 23.3% of its amplitude value. In the short period of time differential stress begin to grow rapidly and at the amplitude value of wave’s propagation reach value of 0 (ζ → 0) which is approximates uniaxial stress and continued decline of amplitude value of wave’s propagation reaches value of negative 1 it is strain step or shear stress relaxation
(ζ → -1) (area Ι, and ΙΙ).

Rock’s dilatant volume increase unconditionally connected to the increase of its permeability by creating new pore channels and increasing existing pore space.

By comparing progressing dilatancy for the strong sandstone depicted in Figure 5 or for the limestone depicted in Figure 6 to the increase in the rock’s permeability we can see its dependence and how it is vary with the rock’s characteristics.

Appropriate application of the exact amount of explosives and the regime of a detonation is the key to optimizing the results of this stimulation technique. The residual positive effect of applying our technique will likely last more than 4 years and should normally increase yields by up to 4 times for oil wells, up to 10 times for gas wells and up to 12 times for irrigation wells.

During post treatment observations no recompression of micro fractured rock has been detected. The SWTorpedo well stimulation services requires the use of only small amounts of explosives resulting in no damage to the casing string. When it is necessary, casing protection is provided.