Rock drillability grade prediction method based on fixed bit pressure

Abstract

The invention discloses a rock drillability grade prediction method based on fixed bit pressure, and the method comprises the following steps: 1, carrying out fixed bit pressure drilling, and obtaining an actual measurement relation curve between the rock breaking depth and the drilling time; 2, according to the relation between the contact area of the drill bit teeth and the rock and the drilling depth, the relation between the drilling depth and the rock breaking volume of the drill bit is obtained; according to the relation between the drilling depth and the rock breaking volume of the drill bit, a theoretical relation curve between the rock breaking depth and the drilling time is obtained; 3, fitting the actual measurement relation curve and the theoretical relation curve to obtain the rock breaking volume in unit time; 4, obtaining the rock breaking time according to the rock breaking volume per unit time obtained in the step 3; obtaining a corresponding rock drillability grade according to the rock breaking time; while the rock drillability grade is accurately deduced and predicted, the number of experimental groups for drillability grading is effectively reduced, the experimental process is simplified, and the rock core and measurement time is saved.

Description

Technical Field

[0001] The invention relates to rock drillability classification, and in particular to a rock drillability grade prediction method based on fixed bit pressure. Background Art

[0002] Rock drillability primarily indicates the ability of formation rock to resist crushing during drilling, reflecting the ease with which the drill bit can break rock. It is an important reference for drill bit selection and optimized cutter design. The concept of rock drillability was first proposed by Tillson in 1927, and AL Head first classified formation drillability in 1951. The test results used a weight on bit (WOB) of 1.86 kN and a rotational speed of 110 r / min, respectively, with an effective drilling depth of 1.59 mm. Based on these test results, rock drillability was categorized into 15 levels. In 1962, Rollow further tested rock drillability using roller cone drill bits.

[0003] In China, the rock drillability test and grading method was first published in 1991. The parameters used, such as drilling pressure, rotation speed, drilling depth, etc., are relatively close to the test values proposed by Rollo. In the following period, with the continuous improvement of the performance of PDC drill bits, their practicality and rock breaking efficiency have been greatly improved, and their market share has also been increasing. For this reason, some scholars suggested using PDC micro drill bits for rock drillability testing. Subsequently, the corresponding standard was released in 2000, which specifically stipulated the model, tooth shape, drilling parameters, etc. of the drill bits used. At the same time, with the continuous increase in drilling depth, the strength of the drilled rock has also continued to increase. Studies have found that for some hard rocks, under standard drilling pressure conditions (500N), micro drill bits are difficult to effectively penetrate the rock and cannot reach the specified drilling depth. Therefore, it is impossible to effectively obtain the rock drillability grade value.

[0004] In existing grading methods, the drilling pressure needs to be gradually increased during the measurement and grading process for hard rock. This requires many experimental groups and a cumbersome process. The PDC cutter needs to continuously improve the drilling pressure and measure the penetration time. In addition, when performing rock drillability grade determination in deep wells, problems such as difficult drilling, long measurement time, and precious and easily damaged cores are usually encountered. Summary of the Invention

[0005] Aiming at the problems existing in the prior art, the present invention provides a rock drillability grade prediction method based on fixed bit weight.

[0006] The technical solution adopted by the present invention is: a method for predicting rock drillability grade based on fixed bit pressure, comprising the following steps:

[0007] Step 1: Drill with constant weight on bit to obtain the measured relationship curve between rock breaking depth and drilling time;

[0008] Step 2: Based on the relationship between the contact area between the drill bit teeth and the rock and the drilling depth, the relationship between the drilling depth and the rock breaking volume of the drill bit is obtained;

[0009] According to the relationship between drilling depth and rock breaking volume of the drill bit, the theoretical relationship curve between rock breaking depth and drilling time is obtained;

[0010] Step 3: Fit the measured relationship curve with the theoretical relationship curve to obtain the rock breaking volume per unit time;

[0011] Step 4: Obtain the rock breaking time based on the rock breaking volume per unit time obtained in step 3; and obtain the corresponding rock drillability grade based on the rock breaking time.

[0012] Furthermore, the relationship between the contact area between the drill bit teeth and the rock and the drilling depth in step 2 is as follows:

[0013]

[0014] Where: S is the contact area, R is the cutter radius, and L is the chordal distance between the cutter and the rock. The calculation method of L is as follows:

[0015] L=Rd / cosθ

[0016] Where: d is the drilling depth, θ is the cutting back angle.

[0017] Furthermore, the relationship between the drilling depth and the rock breaking volume of the drill bit in step 2 is as follows:

[0018]

[0019] Where: V is the rock breaking volume of the drill bit, and a is the distance between the centers of the two cutting teeth.

[0020] Furthermore, the theoretical relationship curve in step 2 is as follows:

[0021]

[0022] Where: v0 is the rock breaking volume per unit time.

[0023] Furthermore, in step 3, the residual value between the theoretical relationship curve and the measured relationship curve is calculated by the least square method, and the rock breaking volume per unit time corresponding to the minimum residual value is obtained.

[0024] Furthermore, the rock drillability grade is calculated as follows:

[0025] K d =log2 T1=log2(2T2)=log22+log2 T2=log2 T2+1

[0026] K d =log2 T3+3

[0027] Where: T1 and T2 are the drilling times corresponding to WOB level 1 and WOB level 2, respectively; T3 is the drilling time corresponding to WOB level 3.

[0028] The beneficial effects of the present invention are:

[0029] (1) Based on the single-tooth rock breaking mechanism, the present invention constructs a drilling depth-time model, selects an appropriate rock breaking amount per unit time to perform optimal fitting on the theoretical calculation curve, maximizes the accuracy of the theoretical calculation curve model, and realizes accurate rock drillability grade determination;

[0030] (2) While accurately deriving and predicting the rock drillability grade, the present invention effectively reduces the number of experimental groups for drillability classification, simplifies the experimental process, and saves core and measurement time. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a schematic diagram of the process of the present invention.

[0032] Figure 2 This is the homogeneous change of cutting force under different cutter-rock interaction areas in the embodiment of the present invention.

[0033] Figure 3 The figure shows the changes of rock drilling curves under different bit pressures in the embodiment of the present invention.

[0034] Figure 4 This is the theoretical calculated value curve when the residual is minimum in the embodiment of the present invention.

[0035] Figure 5 The figure shows the comparison between the experimental test and theoretical calculation of rock drillability in the embodiment of the present invention. DETAILED DESCRIPTION

[0036] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0037] like Figure 1 As shown, a rock drillability grade prediction method based on fixed bit weight includes the following steps:

[0038] Step 1: Drill with constant weight on bit to obtain the measured relationship curve between rock breaking depth and drilling time;

[0039] Step 2: Based on the relationship between the contact area between the drill bit teeth and the rock and the drilling depth, the relationship between the drilling depth and the rock breaking volume of the drill bit is obtained;

[0040] During the rock drillability test, a fixed-weight-on-bit (WOB) PDC drill bit is used to intrude and rotary-cut the rock. A unique feature of this test is that if the drill bit slips and the current WOB is insufficient to crush the rock, there's no need to change the WOB and retest the rock for drillability. According to the single-cutter rock-breaking mechanism, under the drillability test parameters, the cutting depth remains low, and the rock primarily fails plastically. At this point, the cutting force is proportional to the cutter-rock interaction area, and the rock crushing ratio remains constant within this range. These results demonstrate that the rock crushing mechanism remains unchanged, primarily crushing the rock. The resulting rock cuttings are powdery, consistent with the rock cuttings produced during drillability testing. As drilling depth increases, the interaction area between the PDC cutter and the rock increases, reducing the PDC bit's drilling depth within the same timeframe. This can ultimately lead to the drill bit slipping or failure to reach the required drilling depth for rock drillability testing within the specified timeframe.

[0041] The relationship between the vertical pressure force and cutting force during the rock breaking process of PDC teeth can be expressed as:

[0042] F N =F S tan(θ+ψ) (1)

[0043] Where: θ is the back tilt angle of the cutting tooth, ψ is the internal friction angle of the rock, F S is the pressing force, F N is the cutting force.

[0044] In rock drillability testing, the drill bit model and cutter size remain constant, resulting in a constant back rake angle. Furthermore, when drilling the same rock type, the rock's mechanical properties remain constant, ensuring a constant internal friction angle. In this case, the cutter penetration force and cutting force are directly proportional, and the cutting force is proportional to the cutter-rock interaction area within the rock's plastic failure range. Therefore, it can be determined that when the cutter penetration force remains constant, the contact area between the cutter and the rock also remains constant.

[0045] As a drill bit penetrates rock, the penetration force reflects the bit's weight on bit, which is typically held constant at a specified value. Simultaneously, the drill bit's rotational speed is also held constant, so the displacement of the cutting teeth per unit time remains constant. Combined with the cutter-rock interaction area, the rock volume removed per unit time can be determined. Combined with the theoretically required rock removal volume, the drilling time can be calculated.

[0046] Because the back rake angle and the PDC tooth diameter are constant, when the drill bit penetrates the rock at different depths, the contact area between the tooth and the rock is:

[0047]

[0048] Where: S is the contact area, R is the cutter radius, and L is the chordal distance between the cutter and the rock. The calculation method of L is as follows:

[0049] L=Rd / cosθ (3)

[0050] Where: d is the drilling depth, θ is the back rake angle of the cutting tooth.

[0051] The contact area between the teeth and the rock can be calculated by simply knowing the drilling depth.

[0052] Assuming the distance between the two cutting teeth centers is a, the relationship between drilling depth and rock breaking volume of the drill bit is obtained:

[0053]

[0054] Where: V is the rock breaking volume of the drill bit, and a is the distance between the centers of the two cutting teeth.

[0055] According to the relationship between drilling depth and rock breaking volume of the drill bit, the theoretical relationship curve between rock breaking depth and drilling time is obtained:

[0056]

[0057] Where: v0 is the rock breaking volume per unit time.

[0058] It can be seen that the time consumed in drilling at different depths is only related to the rock-breaking volume of the microdrill bit at different drilling depths and the rock-breaking volume per unit time. From Equation (4), it can be seen that the cutting tooth radius R, the distance a between the two cutting tooth centers, and the tooth inclination angle θ are all constant values. The rock-breaking volume of the microdrill bit at different drilling depths is only related to the drilling depth.

[0059] Step 3: Fit the measured relationship curve with the theoretical relationship curve to obtain the rock breaking volume per unit time;

[0060] By continuously adjusting the value of v0 in formula (5) based on the relationship between drilling depth and time, the trend of the theoretical calculated value and the shape of the corresponding curve are changed, and the residual value is continuously calculated using the least squares principle. Ultimately, when v0 is a certain value, the theoretical calculated value and the actual drilling curve fit best.

[0061] Step 4: Obtain the rock breaking time based on the rock breaking volume per unit time obtained in step 3; and obtain the corresponding rock drillability grade based on the rock breaking time.

[0062] The rock drillability grade is calculated as follows:

[0063] K d =log2 T1=log2(2T2)=log22+log2 T2=log2 T2+1 (6)

[0064] K d =log2 T3+3 (7)

[0065] Where: T1 and T2 are the drilling times corresponding to WOB level 1 and WOB level 2, respectively; T3 is the drilling time corresponding to WOB level 3.

[0066] According to the selected fixed bit weight, choose whether to use formula (6) or formula (7) to calculate the corresponding drillability grade.

[0067] The effects of the present invention are described below with specific experimental results. The data in the following figures are all experimental results.

[0068] Figure 2 Figure 1 shows the mean cutting force curves for different cutter-rock interaction areas, with A representing the theoretical cutting force and B representing the actual cutting force. Figure A shows that at low cutting depths, the cutting force increases linearly with increasing interaction area (increasing cutting depth), with a proportionality coefficient of approximately 0.52. Figure B shows that the rate of increase in cutting force slows significantly with increasing cutting depth. This indicates that in the initial stages of rock breaking, the cutting force increases linearly with increasing rock breaking depth. As the cutter-rock interaction area increases deeper into the rock, the rate of increase in cutting force slows significantly.

[0069] Figure 3 The following diagram illustrates rock drilling curves under different drilling pressures. Rock was drilled at pressures of 500N, 1000N, and 2000N. The graph shows similar trends for the rock drilling curves under different drilling pressures. Displacement increases with increasing drilling time, indicating that the drill bit is continuously engaging the rock. Simultaneously, as drilling pressure increases, the drilling speed increases significantly, resulting in a continuous decrease in drilling time. As drilling pressure increases, the corresponding cutting force also increases proportionally, and the amount of rock broken per unit time within the plastic failure range also increases by a corresponding multiple. Consequently, the overall rock breaking speed increases significantly, while the corresponding rock breaking time decreases. When the drilling pressure increases from 500N to 1000N, the rock breaking time decreases by 48.6%, indicating that the rock breaking speed increases by nearly half, almost in line with the increase in drilling pressure.

[0070] The present invention selects a 1000N WOB, and the rock drillability calculated using formula (6) is highly accurate. Experimental test results also show that within the 1000N WOB range, the hard rock crushing mechanism remains unchanged. For some rocks that are difficult to drill with 500N, this is simply because the contact arc length between the cutting teeth and the rock increases with increasing drilling depth. Therefore, even small fluctuations in the tested cutting depth can cause significant changes in the amount of rock broken per unit time. This makes it difficult for the drill bit to further effectively penetrate the rock.

[0071] When the WOB was increased to 2000N, the drilling time decreased by only 18.6% compared to the conventional WOB (500N), and the corresponding ROP increased by 437.5%. This trend is even more significant than the WOB change rate (300%). This is primarily due to the significant increase in rock penetration after the WOB reaches a certain value. This is primarily due to the fact that the contact arc length between the drill bit and the rock is relatively small during the early stages of drilling. Therefore, for a given rock breaking volume per unit time, the cutter's rock penetration depth increases significantly, which can easily lead to a shift in the rock breaking pattern.

[0072] When calculating the rock drillability grade, the required rock breaking volume per unit time is obtained by fitting the data obtained when the drilling depth was shallow in the early stage and combining the theoretical results of formulas (4) and (5). Figure 4 The fitting curve of the theoretical calculation value is when the residual value is minimum. At this time, the fitting degree between the theoretical calculation value and the actual drilling curve is the best.

[0073] Compare the experimental test value of rock drillability with the theoretical calculated value, and substitute the theoretical drilling time when the rock drillability classification standard depth is reached into the drillability grade formula (6) or (7) to obtain the predicted value of the drillability grade.

[0074] Figure 5 The middle scatter points are measured data when drilling granite with a drilling pressure of 1000N. Because granite is extremely strong, as the drilling depth increases in the later stages of drilling, the cutter-rock interaction area increases, making it difficult for the drill bit to further effectively penetrate the rock. However, in the early stages of drilling, the drill bit can penetrate the rock without any obstacles. Therefore, using formulas (4) and (5) to fit Figure 5 As the number of data points increases, the residual value obtained from the observation fitting is not affected. When the residual value begins to increase significantly, it means that the drill bit has not effectively penetrated the rock under the actual drilling data, and the invalid data has interfered with the results. Therefore, the theoretical drilling curve can be obtained by fitting the valid data in the first half of the period, and the theoretical drilling time can be determined. Substituting it into the drillability grade formula (7) can obtain the predicted value of the drillability grade.

[0075] The present invention uses a PDC drill bit with a fixed drilling pressure to measure rock drilling data, simulates the relationship between drilling depth and time through actual test data, and fits the effective drilling data when the PDC drill bit just enters the formation. By fitting the theoretical drilling time, the rock drillability grade can be quickly derived. The rock drillability grade can be predicted based on drilling with a fixed drilling pressure, which can not only accurately predict the rock drillability grade, but also effectively reduce the difficulty of evaluating rock drillability, reduce core loss and significantly reduce evaluation time. Based on this idea, it is proposed to construct a drilling depth and time model, select effective drilling and rock breaking data when drilling with a fixed drilling pressure, and continuously adjust the rock breaking volume v0 per unit time to fit the theoretical calculation value curve with the best fit to the actual drilling curve. It effectively reduces the difficulty of rock drillability evaluation and facilitates the efficient derivation and prediction of rock drillability measurement grade.

Claims

1. A rock drillability grade prediction method based on fixed bit weight, characterized in that: The following steps are involved: Step 1: Drill with constant weight on bit to obtain the measured relationship curve between rock breaking depth and drilling time; Step 2: Based on the relationship between the contact area between the drill bit teeth and the rock and the drilling depth, the relationship between the drilling depth and the rock breaking volume of the drill bit is obtained; According to the relationship between drilling depth and rock breaking volume of the drill bit, the theoretical relationship curve between rock breaking depth and drilling time is obtained; Step 3: Fit the measured relationship curve with the theoretical relationship curve to obtain the rock breaking volume per unit time; Step 4: Obtain the rock breaking time based on the rock breaking volume per unit time obtained in step 3; and obtain the corresponding rock drillability grade based on the rock breaking time.

2. The rock drillability grade prediction method based on fixed bit weight according to claim 1, characterized in that: The relationship between the contact area between the drill bit teeth and the rock and the drilling depth in step 2 is as follows: Where: S is the contact area, R is the cutter radius, L is the chord distance between the cutter and the rock contact chord, and L is calculated as follows: L=Rd / cosθ Where: d is the drilling depth, θ is the back rake angle of the cutting tooth.

3. The rock drillability grade prediction method based on fixed bit weight according to claim 2, characterized in that: The relationship between the drilling depth and the rock breaking volume of the drill bit in step 2 is as follows: Where: V is the rock breaking volume of the drill bit, and a is the distance between the centers of the two cutting teeth.

4. The method for predicting rock drillability grade based on fixed bit weight according to claim 3, characterized in that: The theoretical relationship curve in step 2 is as follows: Where: v0 is the rock breaking volume per unit time.

5. The rock drillability grade prediction method based on fixed bit weight according to claim 1, characterized in that: In step 3, the residual value between the theoretical relationship curve and the measured relationship curve is calculated by the least square method, and the rock breaking volume per unit time corresponding to the minimum residual value is obtained.

6. The rock drillability grade prediction method based on fixed bit weight according to claim 1, characterized in that: The rock drillability grade is calculated as follows: K d =log2 T1=log2(2T2)=log22+log2 T2=log2 T2+1 <h2 style=";text-align:left;direction:ltr">K<h2 style=";text-align:left;direction:ltr"> d <h2 style=";text-align:left;direction:ltr"> =log2 T3+3 Where: T1 and T2 are the drilling times corresponding to WOB level 1 and WOB level 2, respectively; T3 is the drilling time corresponding to WOB level 3.

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