Abstract
The high-voltage electrical pulses (HVEP) technology is the most potential method to improve the rate of penetration (ROP) in deep hard formations. A detailed understanding of the fragmentation mechanism by HVEP is essential to enhance ROP in rock-breaking and to optimize the electrical parameters. However, few pieces of researches are focused on the uneven dielectric properties of rock. This paper uses particle flow code software and Voronoi tessellation to generate granite models with different heterogeneity indexes; the granite models consider the differences in the micro-dielectric properties and particle size of various mineral components. The simulation of the plasma channel growth process, which considers the circuit equations of HVEP and the probabilistic development model, is analyzed. The results show that the concentration of the electric field in the feasible region makes the extreme value of the entire electric field smaller, which puts forward a higher energy demand for the initial breakdown of granite. The finer the grain size of granite, the smaller the broken ratio coefficient, and the better the crushing degree of HVEP. There is almost no difference in the energy efficiency of HVEP between granites with different heterogeneity indexes. The total length of the plasma channel is dominated by “directional self-direction” and “priority of tips”, which is positively correlated with the energy efficiency of HVEP. The research results have definite guiding significance for engineering application of HVEP, bottom hole assembly design, and drilling tool design of HVEP.
Highlights
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This paper mainly established a simulation model of fragmenting granite by high-voltage electrical pulses to investigate the growth mechanism of plasma channels and to explore the difference in electrical breakdown caused by the heterogeneous dielectric properties of granite. The results show that the concentration of the electric field in the feasible region makes the extreme value of the entire electric field smaller, which puts forward a higher energy demand for the initial breakdown of granite; the finer the grain size of granite, the smaller the broken ratio coefficient, and the better the crushing degree of high-voltage electrical pulses; there is almost no difference in the energy efficiency of high-voltage electrical pulses between granites with different heterogeneity indexes. The total length of the plasma channel is dominated by “directional self-direction” and “priority of tips”, which is positively correlated with the energy efficiency of high-voltage electrical pulses
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Abbreviations
- BHA:
-
Bottom hole assembly
- CBE:
-
Complete electric breakdown
- CBS:
-
Complete breakdown strength
- EPF:
-
Electric pulse fragmentation
- EHF:
-
Electro-hydraulic fragmentation
- EBP:
-
Electrical breakdown process
- HVPF:
-
High-voltage electrical pulses
- PFC:
-
Particle flow code
- PDM:
-
Probabilistic development model
- ROP:
-
Rate of penetration
- TRD:
-
Traditional rotary drilling
- TBS:
-
Threshold breakdown strength
- PEB:
-
Partial electrical breakdown
- PCBT:
-
Plasma channel branch tip
- PCT:
-
Plasma channel trunk
- E ex :
-
Energy consumed in the exploding phase
- E 1 :
-
Total energy of a single HVEP
- C :
-
Equivalent capacitance of the circuit
- U P :
-
Peak voltage
- U i :
-
Residual breakdown voltage
- η 1 :
-
Energy conversion efficiency for the breakdown phase
- η 2 :
-
Energy conversion efficiency for the exploding phase
- I(t):
-
Plasma channel current in the exploding phase
- R t :
-
Plasma channel resistance in the exploding phase
- τ i :
-
Time when the breakdown phase ends
- τ b :
-
Time when the exploding phase ends
- E t :
-
Injected plasma channel energy
- η e :
-
Rock-breaking efficiency of EPF
- E i :
-
Partial electric field
- E s :
-
Complete breakdown strength
- E c :
-
Threshold breakdown strength
- n p :
-
Probability index
- P Bi :
-
Development probability of the path to be developed
- τ ti :
-
“Branch” growth time
- ξ i :
-
Probability function of “branch” growth
- k :
-
Constant on the magnitude of “branch” growth time
- ε 0 :
-
Permittivity of vacuum
- ε r :
-
Relative permittivity
- φ :
-
Potential
- ρ q :
-
Space-charge density
- J :
-
Current density vector
- i(t):
-
Circuit current
- L :
-
Equivalent inductance of the circuit
- q(t):
-
Charge in the equivalent capacitance C
- U c :
-
Initial voltage across the equivalent capacitor C
- R z :
-
Equivalent resistance of the circuit
- φ d(t):
-
Potential difference at the junction
- E d :
-
Channel voltage drop field strength
- h* :
-
Feature-length
- R ch :
-
Main channel resistance in the breakdown phase
- H a :
-
Activation enthalpy of molten rock mass
- K :
-
Universal gas constant
- r ch :
-
Radius of the main plasma channel
- T(t):
-
Temperature of the plasma channel
- t :
-
Time
- α :
-
Coefficient of linear expansion
- σ 0 :
-
Arrhenius frequency factor
- σ B :
-
Stefan–Boltzmann constant
- L ch(t):
-
Length of the developed main plasma channel in the exploding phase
- v(t):
-
Growth rate of the main plasma channel
- Rʹch :
-
Main plasma channel resistance in the exploding phase
- K ch :
-
Resistance coefficient
- Lʹch :
-
Length of the plasma channel in the exploding phase
- I i :
-
Current at the end of the breakdown phase
- W ch :
-
Energy injected into the plasma channel
- R a :
-
Average grain size
- ω :
-
Volume fraction of the mineral
- r :
-
Mean particle size of the mineral
- H gran :
-
Heterogeneity index
- L t :
-
Total length of plasma channel
- d a :
-
Average penetration depth
- (X, Y):
-
Coordinate of the developed “tree point”
- (x, y):
-
Coordinate of the last developed “tree point” of the “tree point” (X, Y)
- H 2 :
-
Granite height
- γ :
-
Broken ratio coefficient
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Acknowledgements
This study is supported by the National Natural Science Foundation of China (Grant no. 52034006; no. 52004229), Applied Basic Research of Sichuan Province (Free Exploration-2019YJ0520), Science and Technology Cooperation Project of the CNPC-SWPU Innovation Alliance (2020CX040301). Such supports are greatly appreciated by the authors.
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XZ contributed to the conception of the study; MC contributed significantly to analysis and manuscript preparation; MC performed the data analyses and wrote the manuscript; YL and WL helped perform the analysis with constructive discussions; Hai Hu sorted out relevant references. All the above participants state that the contents of the article does not contain unknown or fake and false data.
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Zhu, X., Chen, M., Liu, W. et al. The Fragmentation Mechanism of Heterogeneous Granite by High-Voltage Electrical Pulses. Rock Mech Rock Eng 55, 4351–4372 (2022). https://doi.org/10.1007/s00603-022-02874-z
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DOI: https://doi.org/10.1007/s00603-022-02874-z