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Experimental measurement of surface temperatures during flame-jet induced thermal spallation

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Summary

Thermal spallation is a method whereby the surface of a rock is rapidly heated causing small (100–1000 μm) flakes or spalls, to form. When applied to drilling, a supersonic, high temperature (2600 K) gas jet is directed at the rock to provide the heat source and sweep away the spalls.

Previous studies of thermal spallation drilling indicate that penetration rates of up to 30 m/hr (100 ft/hr), approximately ten times greater than commonly obtained using conventional rotary mechanical methods, can be achieved in competent, non-fractured hard rock such as granite. A total direct operating cost for drilling in granite using a flame-jet spallation drill was estimated by Browning (1981) to be approximately $9/m in 1991$ (about $3/ft) compared to “trouble-free” well drilling costs for conventional rotary methods in similar rock to depths of 3 to 7 km (10000 to 21000 ft) of $300 to $900/m ($100 to $300/ft) (Tester and Herzog, 1990, 1992). The Browning estimates for spallation drilling are obviously optimistic in that they don't include capital costs for the rig and associated hardware. However, the substantially higher penetration rates, significantly reduced wear of downhole components, and the high efficiency of rock communition in comparison to rotary methods suggest that substantial cost reductions could be possible in deep drilling applications. For example, in the construction of hot dry rock geothermal power plants where rotary mechanical methods are used for well drilling to depths of (4 to 5 km), about half of the initial capital cost would be required for well drilling alone (Tester and Herzog, 1992).

The current study has focused on gaining a better understanding of both the rock failure mechanism that occurs during thermal spallation and the heat transfer from the gas jet to the rock surface. Rock mechanics modeling leads to an expression for the surface temperature during spallation as a function of rock physical properties and the incident heat flux. Surface temperature measurements and heat flux determination during laser and flame-jet induced thermal spallation are used to provide appropriate values of the “Weibull parameters” that statistically describe the size-strength relationship in granite. Use of these parameters allows one to accurately estimate surface temperatures required by the numerical simulation model to calculate heat and mass transport rates occurring in the flow field above the spalling rock surface.

Based on the results of this experimental study, we concluded that mechanically-determined Weibull parameters are not directly applicable to describe spallation failure phenomena caused by thermal stress. Under the extreme rapid heating conditions of flame-jet drilling, local overheating and possibly stress relief lead to higher temperatures than predicted using room temperature Weibull parameters. Nonetheless, the Weibull-based statistical model of failure can be utilized by empirically fitting them and σ0 Weibull parameters to match experimental measurements of spalling surface temperature as a function of applied heat flux. Correlations for steady state and onset spallation conditions were established with consistent results obtained for both laser and propane-oxygen flame jet heating.

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Abbreviations

A :

slope of best-fit line

C L :

spall diameter: thickness ratio

C P :

constant pressure heat capacity (J/kg K)

E :

Young's modulus (MPa); total energy

G(σ):

cumulative probability of failure

ΔH pt :

energy losses due to miscellaneous phase transitions and crack formation (W/m2)

k r :

rock thermal conductivity (W/m K)

m :

Weibull homogeneity parameter

Q r ,Q :

local heat flux to rock (W/m2)

Q p :

predicted heat flux (W/m2)

Q jet :

total jet inlet heat flux (w/m2)

R noz :

nozzle radius (m)

R h :

hole radius (m)

SOD :

dimensionless stand-off distance (Z dr /R dr )

St :

stanton number

St p :

predicted Stanton number based on surface heat flux

St exp :

experimental Stanton number based on measured penetration rate

t :

time (s)

T :

temperature (K)

T s :

local surface temperature (K)

T ro :

initial rock temperature (K)

T s, st :

stagnation point surface temperature (K)

T jet :

gas temperature at nozzle outlet (K)

U dr :

local drilling velocity normal to rock surface (m/s)

U jet :

jet velocity (m/s)

V :

sample volume (m3)

V dr :

forward drilling or penetration rate (m/s)

Z dr :

distance from the bottom of the drill to the stagnation point (m)

α r :

thermal diffusivity of the rock (m2/s)

β r :

thermal coefficient of expansion (V −1 (δV/δT)ρ (K −1)

σ:

local rock stress (MPa)

σ0 :

Weibull parameter (MPa-m3/m)

ρ r :

rock density (kg/m3)

ν:

Poisson's ratio

dr :

drilling related parameters

exp:

experimental value

jet:

property at nozzle outlet conditions

noz:

at nozzle

r :

rock property

s :

rock surface property

sp :

at spallation

st :

at stagnation point conditions

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  1. J. W. Tester

    Present address: Energy Laboratory and Chemical Engineering Department E40-455, Massachusetts Institute of Technology, 02139, Cambridge, MA, U S A

Authors and Affiliations

  1. Energy Laboratory and Chemical Engineering Department E40-455, Massachusetts Institute of Technology, 02139, Cambridge, MA, U S A

    M. A. Wilkinson

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Wilkinson, M.A., Tester, J.W. Experimental measurement of surface temperatures during flame-jet induced thermal spallation. Rock Mech Rock Engng 26, 29–62 (1993). https://doi.org/10.1007/BF01019868

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