The Changes to the Rock Physical and Mechanical Properties Near the Hole Produced by Successive Impacts of a Steel-Particle Water Jet: A Case Study in a Tight Sandstone

Abstract

Particle impact drilling (PID) is a promising technology to enhance the rate of penetration in hard and abrasive formations. The changes to physical and mechanical properties near the crater of a full-size tight sandstone sample after successive impacts of a steel-particle water jet are investigated by different scales of rock physics measurements to estimate the range of the damage zone. Similar measurements are also carried out on a sample from the same formation without steel-particle water jet as a reference. The results indicate that: (i) there is a damage zone around the crater with induced cracks and pore collapse caused by the impact stress wave produced by the steel-particle water jet. The dimensionless depth of the damage zone from the crater’s surface is about 0.69 times the jet diameter (d₀). Within the damage zone, the dense compaction zone is just near the crater surface within a dimensionless distance of about (0.02–0.06) d₀, where the porosity and the permeability slightly decrease, and show significant strength decrease. (ii) The changes of the porosity and the P- and S-wave velocities after steel-particle water jet at core scale are neglectable. Compared to the reference sample, the permeability at the lateral of the crater is (4.52–30.90) times higher, while the permeability beneath the bottom of the crater is 79% lower. The uniaxial compressional strength (UCS) decreases by 15.6%–65.7%. (iii) The indentation hardness after particle jetting shows a significant decrease. The macro-indentation hardness decreases from 1.92 GPa to 1.30 GPa at core scale. Within the damage zone, the hardness and the Young’s modulus calculated from nanoindentation tests decrease with the increase of the distance to the crater’s surface. This work as a case study provides new experimental evidence of the evolution of rock damage by the impact stress of the steel-particle water jet.

Highlights

• The dimensionless depth of the damage zone from the crater’s surface is about 0.69 times jet diameter.

• Permeability is (4.52–30.90) times higher at the laterals of the crater.

• Macro-indentation hardness and UCS decrease significantly in the damage zone.

• Nanoindentation hardness decreases with its distance to the crater’s surface.

Appendix A: Theory Models for Nanoindentation Analysis

For our nanoindentation test, the loading and unloading rate is constant, which could be treated as quasi-static. Figure

Fig. 11

Nanoindentation schematic diagrams (after Cheng et al. 2022). a is the variation of load with time. The loading and unloading rates are kept constant. The maximum load holds for 2.0 s. b is the typical displacement—load curve. The stiffness of the contact (S) is equal to the initial slope of unloading curve

11 shows the typical load and displacement curves for nanoindentation tests. A widely used method for the explanation of nanoindentation data is proposed by Oliver and Pharr (1992). The nanoindentation hardness (H_n) could be calculated as:

$$H_{{\text{n}}} = \frac{{P_{\max } }}{{A_{{\text{c}}} }},$$

(A1)

where, P_max is the maximum load, and A_c is the projected area of contact at the maximum load. Oliver and Pharr (1992, 2004) proposed that A_c is a function of the contact depth (h_c) and the shape of the indenter tip. For the Berkovich tip (θ = 142°) used in our test,

$$A_{{\text{c}}} = 3\sqrt 3 h_{{\text{c}}}^{{2}} \tan^{2} \theta \approx 24.5h_{{\text{c}}}^{{2}} .$$

(A2)

The contact depth could be calculated as (Oliver and Pharr 1992)

$$h_{{\text{c}}} = h_{\max } - \varepsilon \frac{{P_{\max } }}{S},$$

(A3)

where, h_max is the maximum displacement of the indenter at P_max; ε = 0.75 for the Berkovich tip; and S = dP/dh is the stiffness of the contact which is equal to the initial slope of unloading curve (Fig. 11b).

The reduced Young’s modulus (E_r)is calculated based on the Hertz’s elastic contact theory:

$$E_{{\text{r}}} { = }\frac{\sqrt \pi }{{2\beta }}\frac{S}{{\sqrt {A_{{\text{c}}} } }},$$

(A4)

where, β is related to the shape of indenter tip, β = 1.0 for sphere, and β = 1.034 for the Berkovich tip. E_r could be estimated by the effective Young’s modulus of two contacted spheres (Mindline 1949):

$$E_{{\text{r}}} = \frac{{1 - v_{1}^{2} }}{{E_{1} }} + \frac{{1 - v_{2}^{2} }}{{E_{2} }},$$

(A5)

where, E₁ and E₂ are their Young’s moduli, v₁ and v₂ are their Poisson’s ratios. For the nanoindentation, the indenter tip (diamond, E₂ = 1140 GPa, v₂ = 0.07) and the test sample are the two contact bodies. The identification of S and A_c allows E_r to be calculated, and then the (1-v₁²)/E₁ for the test sample is obtained (Oliver and Pharr 1992; Cheng et al. 2022).