METHOD FOR EVALUATING ROCK DRILLABILITY BY NANO-INDENTATION TEST ON ROCK CUTTING

Abstract

A method for evaluating rock drillability by a nano-indentation test on a rock cutting includes: conducting a nano-indentation test on a rock cutting sample, acquiring a displacement-load curve of an indenter, and calculating a micro-hardness under the nano-indentation test; calculating mineral composition of the rock cutting sample based on a statistical distribution characteristic of the micro-hardness, and transforming the micro-hardness under the nano-indentation test on the rock cutting sample into a macro-hardness; and calculating a rock drillability grade characterized by the micro-hardness under the nano-indentation test on the rock cutting sample based on a correlation between the macro-hardness of the rock cutting sample and the rock drillability grade. In the context of few downhole rock samples and high cost, the method overcomes the limitation of sample size and shape on conventional testing and solves the difficult problem of mechanical parameter testing of deep rocks.

Claims

1. A method for evaluating rock drillability by a nano-indentation test on a rock cutting, comprising the following steps: (1) conducting a nano-indentation test on a rock cutting sample, and calculating a micro-hardness of each of indentation points of the rock cutting: wherein, the micro-hardness of each of the indentation points under the nano-indentation test on the rock cutting sample is calculated as follows: $\begin{array}{cc}{H}_n=\frac{P_m}{A_c}& \left(1\right)\end{array}$ $\begin{array}{cc}{A}_c=24.56h_c^2& \left(2\right)\end{array}$ wherein, H.sub.n denotes the micro-hardness of each of the indentation points under the nano-indentation test on the rock cutting sample, Pa; P.sub.m denotes a maximum indentation load applied in the nano-indentation test, N; A.sub.c denotes a projected area of a contact zone between an indenter and the rock cutting sample, m.sup.2; and h.sub.c denotes an indentation depth, m; (2) calculating a proportion of each of mineral components of the rock cutting sample, and establishing a transformation relationship between the micro-hardness under the nano-indentation test and a macro-hardness, wherein the rock cutting sample is a combination of the mineral components in different proportions, and the micro-hardness varies obviously at different indentation points based on the different proportions of the mineral components under the nano-indentation test on the rock cutting sample; the macro-hardness of the rock cutting sample is calculated as follows: $\begin{array}{cc}H=\stackrel{p}{\underset{i=1}{.Math.}}{\rho }_i{H}_i& \left(3\right)\end{array}$ wherein, H denotes the macro-hardness of the rock cutting sample, Pa; p denotes a category number of the mineral components constituting the rock cutting sample; ρ.sub.i denotes a weight of an i-th mineral component of the mineral components; and H.sub.i denotes a micro-hardness of the i-th mineral component reflected by the nano-indentation test, Pa; and (3) establishing a regression model between the micro-hardness of the rock cutting sample under the nano-indentation test and the rock drillability based on a relationship between the macro-hardness of the rock cutting sample, the micro-hardness under the nano-indentation test, and the rock drillability; wherein a regression model between the macro-hardness of the rock cutting sample and the rock drillability is as follows:
k.sub.d=aH+b  (4) wherein, k.sub.d denotes the rock drillability for a roller cone bit; H denotes the macro-hardness of the rock cutting sample, MPa; and a and b denote regression coefficients.

2. The method according to claim 1, wherein in step (1), the rock cutting sample is specifically prepared as follows: S11: collecting a target rock cutting, and grinding the target rock cutting to a size of a mold to obtain a ground rock cutting with a diameter Φ<25 mm and a height h<20 mm; S12: inserting the ground rock cutting into the mold, injecting epoxy resin to fully contact the ground rock cutting, letting the ground rock cutting stand for at least 24 hours, and obtaining a cemented rock cutting sample after the epoxy resin is completely consolidated; S13: de-molding the cemented rock cutting sample, and polishing a loading surface of the cemented rock cutting sample by a polishing machine to remove the epoxy resin on the loading surface of the cemented rock cutting sample to obtain a polished rock cutting sample; S14: subjecting the polished rock cutting sample in step S13 to a secondary grinding by a sand disc and a diamond suspension until the diamond suspension is gradually fined from 9 μm and 3 μm to 1 μm in terms of a particle size to obtain a further-ground rock cutting sample, wherein an upper end surface of the further-ground rock cutting sample and a lower end surface of the further-ground rock cutting sample are parallel to each other, and a loading surface of the further-ground rock cutting sample becomes a smooth, high-quality interface; and S15: surface-cleaning the further-ground rock cutting sample in step S14 with an organic solvent, drying the further-ground rock cutting sample in an oven to form the rock cutting sample, and sealing the rock cutting sample for storage.

3. The method according to claim 1, wherein in step (1), the nano-indentation test specifically comprises: loading the rock cutting sample by the indenter at a constant loading rate of 20 N/min until a maximum load of 400 μN, then unloading, deriving a load and loading depth changes, and drawing displacement-load curves for 200 indentation points under the nano-indentation test.

4. The method according to claim 1, wherein step (2) specifically comprises: S21: drawing a frequency distribution histogram of the micro-hardness under the nano-indentation test based on a calculation result, conducting a peak analysis, and calculating an interval weight, wherein each peak in the frequency distribution histogram represents a mineral component; the micro-hardness is reasonably divided into different intervals according to the peak; and since each of the mineral components has a different micro-hardness range, ranges of the divided intervals are allowed to be different; S22: calculating a weighted mean of each of the divided intervals as the micro-hardness of each of the mineral components; and S23: weighing and calculating the macro-hardness of the rock cutting sample according to a micro-hardness calculation result of each of the mineral components; wherein, the weight of each of the mineral components of the rock cutting sample is calculated as follows: $\begin{array}{cc}{\rho }_i=\frac{N_i}{N_0}& \left(7\right)\end{array}$ wherein, N.sub.i denotes a number of indentation points in a micro-hardness interval of the i-th mineral component; and N.sub.0 denotes a total number of the indentation points of the rock cutting sample; the micro-hardness of each of the mineral components of the rock cutting sample is calculated as follows: $\begin{array}{cc}{H}_i=\frac{\underset{j=1}{\overset{m}{.Math.}}{H}_{j‐\mathrm{avg}}}{m}=\frac{\underset{j=1}{\overset{m}{.Math.}}\left(\underset{n=1}{\overset{n_j}{.Math.}}{H}_n/n_j\right)}{m}& \left(6\right)\end{array}$ wherein, H.sub.i denotes the micro-hardness of the i-th mineral component reflected by the nano-indentation test, Pa; m denotes a number of secondary intervals divided in the micro-hardness interval of the i-th mineral component; n.sub.j denotes a number of indentation points in a j-th secondary interval of the secondary intervals, n.sub.j≠0; H.sub.j-avg denotes an arithmetic average of a micro-hardness in the j-th secondary interval; and N.sub.i denotes the number of the indentation points in the micro-hardness interval of the i-th mineral component, $N_i=\underset{j=1}{\overset{m}{.Math.}}{n}_j.$

5. The method according to claim 1, wherein in step (3), the regression model between the micro-hardness of the rock cutting sample under the nano-indentation test and the rock drillability is: $\begin{array}{cc}{k}_d=a\underset{i=1}{\overset{p}{.Math.}}{\rho }_i{H}_i+b& \left(5\right)\end{array}$ wherein, k.sub.d denotes the rock drillability for the roller cone bit; p denotes the category number of the mineral components constituting the rock cutting sample; ρ.sub.i denotes the weight of the i-th mineral component; H.sub.i denotes the micro-hardness of the i-th mineral component reflected by the nano-indentation test, MPa; and a and b denote the regression coefficients.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0042] FIG. 1 is a flowchart of a method for evaluating rock drillability by a nano-indentation test on a rock cutting according to the present disclosure;

[0043] FIG. 2 shows collected rock cuttings;

[0044] FIG. 3 shows prepared rock cutting samples;

[0045] FIG. 4 is a displacement-load curve during loading and unloading;

[0046] FIG. 5 shows a surface deformation of the rock cutting sample under different loading and unloading states;

[0047] FIG. 6 shows a displacement-load curve in the nano-indentation test; and

[0048] FIG. 7 shows an analysis of a micro-hardness peak at each indentation point in the nano-indentation test.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0049] Specific implementations of the embodiments of the present disclosure are described below with reference to the drawings. It should be understood that the implementations described herein are merely intended to illustrate and interpret the present disclosure, rather than to limit the present disclosure.

[0050] A method for evaluating rock drillability by a nano-indentation test on a rock cutting includes the following steps: S11: Collect a target rock cutting, and grind the target rock cutting to a size of a mold, so as to obtain a rock cutting with a diameter Φ<25 mm and a height h<20 mm. There should be no obvious cracks on the surface of the polished rock cutting, as shown in FIG. 3.

[0051] S12: Insert the ground rock cutting into the mold, inject epoxy resin to fully contact the rock cutting, let the rock cutting stand for 24 hours or more, obtain a cemented rock cutting sample after the epoxy resin is completely consolidated, surface-clean the rock cutting sample with an organic solvent, dry the rock cutting sample to form the rock cutting sample, and seal the rock cutting sample for storage.

[0052] S13: De-mold the cemented rock cutting sample and polish a loading surface of the rock cutting sample by a polishing machine so as to remove the epoxy resin on the loading surface of the rock cutting sample.

[0053] S14: Subject the rock cutting sample polished by the polishing machine to secondary grinding by a sand disc and a diamond suspension until the diamond suspension is gradually fined from 9 μm and 3 μm to 1 μm in terms of particle size, such that upper and lower end surfaces of the rock cutting sample are parallel to each other, and the loading surface becomes a smooth, high-quality interface.

[0054] S15: Surface-clean the rock cutting sample ground in step S14 with an organic solvent, dry the rock cutting sample in an oven to form the rock cutting sample, and seal the rock cutting sample for storage.

[0055] S16: Carry out a nano-indentation test with a diamond indenter, load the rock cutting sample at a constant loading rate of 20 N/min to a maximum load of 1,000 μN, unload, and automatically record load and loading depth changes in a system.

[0056] S17: Indent multiple times by the indenter by a lattice method on the loading surface of the rock cutting sample and derive displacement-load curves for a total of 200 indentation points, as shown in FIG. 6.

[0057] S18: Determine a maximum indentation load P.sub.m and a maximum indentation depth h.sub.m on the displacement-load curve, and calculate the micro-hardness of the rock cutting sample corresponding to the displacement-load curve of each indentation point.

[00007]$\begin{array}{cc}{H}_n=\frac{P_m}{A_c}& \left(1\right)\end{array}$$\begin{array}{cc}{A}_c=24.56h_c^2& \left(2\right)\end{array}$

[0058] In the Eqs., H.sub.n denotes the micro-hardness of the indentation point under the nano-indentation test on the rock cutting sample, Pa; P.sub.m denotes the maximum indentation load applied in the nano-indentation test, N; A.sub.c denotes a projected area of a contact zone between an indenter and the rock cutting sample, m.sup.2; and h.sub.c denotes an indentation depth, m.

[0059] S21: Draw a frequency distribution histogram of the micro-hardness based on the calculation results, conduct peak analysis, and calculate an interval weight, where each peak in the frequency distribution histogram represents a mineral component, and the micro-hardness is reasonably divided into different intervals according to the peak.

[0060] The interval weight is calculated as follows:

[00008]$\begin{array}{cc}{\rho }_i=\frac{N_i}{N_0}& \left(7\right)\end{array}$

[0061] where, N.sub.i denotes a number of indentation points in the micro-hardness interval of the i-th mineral component, and N.sub.0 denotes a total number of indentation points of the rock cutting sample.

[0062] S22: Calculate a weighted mean of each interval as a micro-hardness of the mineral component.

[0063] The micro-hardness of the mineral component of the rock cutting sample is calculated as follows:

[00009]$\begin{array}{cc}{H}_i=\frac{\underset{j=1}{\overset{m}{.Math.}}{H}_{j‐\mathrm{avg}}}{m}=\frac{\underset{j=1}{\overset{m}{.Math.}}\left(\underset{n=1}{\overset{n_j}{.Math.}}{H}_n/n_j\right)}{m}& \left(6\right)\end{array}$

[0064] where, H.sub.i denotes the micro-hardness of the i-th mineral component reflected by the nano-indentation test, Pa; m denotes a number of secondary intervals divided in the micro-hardness interval of the i-th mineral component, preferably 3 to 5; n.sub.j denotes a number of indentation points in a j-th secondary interval, n.sub.j≠0; H.sub.j-avg denotes an arithmetic average of the micro-hardness in the j-th secondary interval; and N.sub.i denotes the number of indentation points in the micro-hardness interval of the i-th mineral component,

[00010]$N_i=\underset{j=1}{\overset{m}{.Math.}}{n}_j.$

[0065] S23: Weigh and calculate the macro-hardness of the rock cutting sample according to a micro-hardness calculation result of each mineral component.

[00011]$\begin{array}{cc}H=\stackrel{p}{\underset{i=1}{.Math.}}{\rho }_i{H}_i& \left(3\right)\end{array}$

[0066] where, H denotes the macro-hardness of the rock cutting sample, Pa; p denotes a category number of mineral components constituting the rock cutting sample; ρ.sub.i denotes a weight of an i-th mineral component; and H.sub.i denotes the micro-hardness of the i-th mineral component reflected by the nano-indentation test, Pa.

[0067] S31: Establish a regression model between the micro-hardness of the rock cutting sample and rock drillability based on a relationship between the macro-hardness of the rock cutting sample, the micro-hardness under the nano-indentation test, and the rock drillability; and calculate a rock drillability grade.

[0068] The regression model between the macro-hardness of the rock cutting sample and the rock drillability is:

k.sub.d=0.0006H+5.2648  (8)

[0069] Eq. (3) is substituted into Eq. (8) to obtain the regression model between the micro-hardness of the rock cutting sample and the rock drillability:

[00012]$\begin{array}{cc}{k}_d=0.0006\underset{1}{\overset{i}{.Math.}}{\rho }_i{H}_i+5.2648& \left(9\right)\end{array}$

[0070] where, k.sub.d denotes the rock drillability for the roller cone bit; i denotes the categories of mineral components; ρ.sub.i denotes the weight of the i-th mineral component; and H.sub.i denotes the micro-hardness of the i-th mineral component reflected by the nano-indentation test, MPa.

[0071] S32: Derive a rock drillability result according to the above parameters, as shown in Table 1.

TABLE-US-00001 TABLE 1 Rock drillability evaluated by the nano-indentation test Weighted mean Micro- Interval/ hardness within Interval hardness Drillability GPa the interval H.sub.i/GPa weight r.sub.i H/GPa grade k.sub.d (0.06, 0.36) 0.26 0.114 0.946 5.8324 (0.36, 0.56) 0.44 0.332 (0.56, 0.76) 0.65 0.152 (0.76, 1.12) 0.90 0.147 (1.12, 1.36) 1.25 0.082 (1.72, 2.36) 2.01 0.103 (3.00, 3.40) 3.23 0.071

TABLE-US-00002 TABLE 2 Peak micro-hardness at the indentation point Full width at Weighted Fitted half maximum Maximum mean center peak area SN Type Fitted peak area (FWHM) height (WMC) percentage 1 Gaussian 0.00246 0.07718 0.02996 0.22808 7.22389 2 Gaussian 0.01333 0.1394 0.08985 0.4153 39.13276 3 Gaussian 0.00597 0.11314 0.04961 0.62171 17.53742 4 Gaussian 0.00226 0.07177 0.02958 0.87177 6.63379 5 Gaussian 0.00356 0.22241 0.01505 1.25084 10.46078 6 Gaussian 0.00202 0.12709 0.01493 1.87998 5.92794 7 Gaussian 0.00446 0.29327 0.01428 3.21631 13.08342