Fracture Mechanism and Drillability Fractal Method of Roller Bits

The study of rock fracture mechanism is an important branch of oil drilling engineering. It mainly studies the interaction between drill bit and formation rock and the fracture law of rock, which is one of the basic factors determining drilling efficiency. At present, the way to determine the drillability index is to test the drillability index by using the micro drill bit to test the mechanical properties of the rock sample indoors or to simulate the actual drilling conditions. The micro-drill method has a high degree of conformity, but since the indoor test lags behind the actual drilling, the cost is high and the cycle is long, which hinders the improvement of the drilling speed. In order to solve the above problems, the fractal theory is introduced, and a test method for determining the drillability level value by using the fractal dimension of the chip size distribution is proposed, which is called the fractal method.

The method takes the debris from the bottom of the well as the research object, and can be measured while sampling, realizing the measurement while drilling, and fundamentally solving the shortcomings of the traditional coring method, such as hysteresis and high cost. At the beginning of 2006, the author's research has achieved certain results. See, the article is on the basis of this work.

Fractal Concept Fractal Geometry is a new method for quantitatively studying and describing extremely irregular and seemingly disordered complex structures, phenomena or behaviors in nature. The main content is to study some irregular curves and shapes with self-similarity; Irregular patterns with self-reversal; fractal transformations with self-squared and fractal sets with self-affine, and so on. Since there is no feature scale, the fractal can't be measured by general measures (such as length, width, height, etc.). The characteristic parameters describing the fractal are called fractal dimension, which is called fractal dimension, and is represented by D. The basic feature of fractals is self-similarity, and self-similarity or scale invariance in nature is often statistically significant. In practical applications, this self-similarity can be a mathematically strict self-similarity or a "quasi-self-similarity."

The geometrically inconspicuous self-similarity is usually transformed into the statistical self-similarity. The sandstone fractures studied in this paper are self-similar in statistical sense.

Fractal Geometry on the establishment of the 1970s, quickly applied physics, geography, metallurgy, materials science and computer graphics field. In the 1980s, fractal geometry was widely used in rock mechanics, for example, in structural rock mass blasting fractals, mine rock fracture structure fractals, rock fractal strength theory, rock fractures, rock damage fractals, etc. The problem of rock fragmentation during drilling can be described by the fractal theory to describe the fractal law of the returning debris on the well, and then determine the difficulty of rock fragmentation.

2 The bituminous crusher of the roller cone bit The bit used in the oil drilling is divided into three categories: scraper bit, roller bit bit and diamond material bit. The roller bit accounts for 80% ~ 90% of the total footage. The drill bit selected is the roller cone bit and the formation lithology is sandstone. See known rock * Fund Project: the National Natural Science Foundation of China (50474093); China National Petroleum Corporation young Technology Innovation Fund (03E703).

◎ Introduction to the test. The iron supervisor was born in 57 years. Mainly from the oil and gas well engineering information technology, rock mechanics and special drilling technology research students. <The deep sandstone debris of the hot deep S-97 well, although the size is not e! c shape each ublishing by 0. It can be seen that the i-eserv particle size is larger than r, the number of rock particles N and r become a power law relationship at some time t The mass distribution function of sandstone crumbs with particle size x is M(xt). During the 1Jdt period, the mass of sandstone debris with particle size between x and x+dr is the mass of the crumb. The mass of the sandstone can be divided into two parts: the sandstone crumb is broken at the rate S(x) into the next-stage particle size and The sandstone crumb of particle size a is broken into the mass of sandstone crumb with particle size between x and x + dx. 0/Btdx 1 then equation (6) becomes kt=x. 'x,. Equivalent to metric size, you can assume x,. = Visible, the mass distribution of the cuttings obtained by the crusher sandstone is fractal. From the formula (1), the D expression of the sandstone crushing body can be obtained. The equal probability sandstone crushing mechanism of the sandstone crushing body is taken as the test object. The well is located in the southeastern fault depression area of ​​the Songliao Basin. In the ascending structure of the Weizi fault depression, the upper returning debris was obtained from the fractured formation rock by the tri-cone bit. The layer was taken from 3270~3520m, and the lithology was dominated by sandstone, shale and mudstone. Sampling every 10m, the mass of each sample is about 200g, naturally dry, lithological description, bagging and recording depth.

The fracture form of the bottom trident bit is mainly impact, crushing and shearing. The shearing action applied to soft and medium hard formations is achieved by the slipping of the super-top, compound cone and shifting shaft of the conical cone top. The rock-breaking products are mostly flaky rock cuttings. The equal fracture probability of the Zhongsheng32 cuttings is different in size and shape, but from the macroscopic point of view, there is at least one approximate triangular pyramid. From the geometric point of view, using the variation of the triangular cone to simulate the rock crushing process, there are: under the action of the drill teeth, the rock is broken by a large triangular rock with a linear similarity ratio of 1/3. Broken into several similar small triangular stones, which are broken again into smaller triangular stones due to the friction between the broken debris particles, the extrusion, or the collision with the drill bit. Carry out in a certain scale range. This process can use the following equation to describe the number of fracture bases as “the next unit is broken into B3 subunits. If they are divided into easily breakable unit Nf and unbroken solid unit A, Zhao Zhongyan further proved that the fractal dimension has nothing to do with the shape of the broken body. Note that £= household '3, formula (10) can be changed to D, and also related to B of each level of crushing unit. Among them, B=23,4...,m It can be seen from the above that when the rock breaking unit base B=2, the initial value is too large; and when B=45 or the value is larger, P(. is smaller and closer to 0 and too close, so the rock breaking unit base B =3 is the most appropriate. When B is determined, P(. is an exponential equation that increases as D increases. When P(.=0.5, the critical state of fracture and unbroken volume, ie D = 237, is the critical fracture fractal dimension. .

The P of the rock is a manifestation of the ability of the bit to break the rock and is also a sign of the overall fragmentation of the group.

The equal fracture probability of rock varies with the fractal home. 33 Rock crusher experimental results The 25 sets of rock chip samples were sieved one by one and calculated according to formula (4). D. Experimental results show that the statistical correlation coefficient is Above 096, the correlation is extremely high, D varies between 22 and 26. The roller cone bit is rocky P (. is distributed between 0 3 and 07, see, C is a constant. Equation (13) summarizes all D The relationship between the particle size distribution of the value and the energy consumption of the fracture. When the value of D is 2 25 and 3, the integral of the formula (13) is obtained by the rock fracture ratio. The specific work expression of the Ritthger is the new surface theory. The expression d is the initial particle size mm. The crushing ratio Gongsan University said that in explaining the way the crushing energy consumption acts on the rock, but in the fractal model, the energy consumption differential expression is broken. The test shows that the deepening of the 2- 7 well cuttings The D variation interval approximates the Bond crack theory and the fracture mechanism. It can be seen that the effect of energy consumption on the cuttings is mainly used to increase the crack and break the rock debris.

Table 1. Experimental results of Table 1. Experimental studies show that the crushing process of sandstone debris is divided into two stages: (1) under low confining pressure, it breaks into cracks along the cementing zone, and the sand remains intact. (2) With the increase of confining pressure, the fracture is broken into pores, the sand particles are in contact with each other, and high compressive stress is generated at the contact. The sand is broken along the crystal or through the crystal, which is difficult to break. The increase is in scope. Since the upper returning cuttings are taken from 3270 to 3520 m, the confining pressure of the formation rocks is large, and the energy consumption per unit volume of the bit crushing increases, and the rock drillability level increases for the drill bit, and the crushing volume per unit time is reduced. Small, the particle size becomes smaller. The grain size of the cuttings tends to the fine grain end, resulting in a higher fractal dimension.

4 The relationship between the energy consumption of crushing and the particle size distribution of the crushed rock The fractal expression of the crushing energy consumption of the cuttings is the relationship between the fractal dimension of the sandstone crushing body and the drillability. Bookmark4 is well known, the rock drillability value Kd and micro-drilling The relationship between T and T shows that there is an approximate proportional relationship between sandstone fracture D and sandstone compressive strength. The author's research found that there is an approximate proportional relationship between the core intrusion strength Py, the micro drill bit drillability value Kd and the rock fracture body D. P, and Kd are important descriptive parameters of rock drillability, and rock fracture D establishes a relationship with them, which is related to rock drillability. It is determined by the fact that the work is equal to the chip size of the power (W) and the time (s). N is the power required to crush the rock by the roller cone bit, N = CPnDh, P is the weight of the drill, n is the speed, and Dh is the diameter of the drill.

00) At this point, establish a functional relationship between D and Kd. According to the indoor micro-bit test, the grading standard represented by D is as follows: 1~(21)4 is soft in the table; 5~8 is medium; 9~ Level 11 is hard.

Table 2 Fractal Dimension Characterization of Drill Bits Drillability Grades The data in Table 2 are derived from the core of the Songliao Basin. The cuttings D increase with the increase of Kd, and D and Kd have obvious correspondence. The D of a certain interval represents the size of different Kd, and the size interval is appropriate. Since the PDC bit cuttings and the roller bit cuttings are very different in scale and distribution, the specific distribution interval of the classification table needs further study.

5 On-site accuracy test The formation drillability prediction software compiled by the drillability fractal model (21) is used to prepare the corresponding measurement tools, and the Shengping structure of the Xujiaweizi fault depression belt in the southeast fault depression area of ​​the Songliao Basin and the central fault of the Songliao Basin In the ridge area, the Anda-Zhuzhou anticline and the three wells in the northern part of the Gulong fault depression in the western faulted area of ​​the Songliao Basin were sampled and tested. A total of 75 samples were taken. The test items were: indoor micro-drill test of core, fractal dimension of test cuttings and fractal dimension of upper returning debris. The experimental results show that: (1) There is a linear correlation between D and Kd in the rock sample, and the correlation factor is 0826. (2) The core D is broken and the error fluctuation between D and D in the scale is 2% ~ 11%. The overall average value is 608%; the error fluctuation between the D and the D in the grading table is 1% to 9%, and the overall average is 4.19%; (3) The prediction result of the sandstone in the experiment is obvious. It is higher than the predicted values ​​of mudstone and shale, resulting in an increase in the overall prediction error. According to the above experimental results, the author has made corresponding corrections to the rating table, so that the accuracy is further improved.

6 Conclusion The sandstone fracture body of the roller cone bit is fractal, and under the assumption of equal probability, the deep sandstone fracture body D is larger than the mudstone and shale D. The measured results prove that the fracture is similar to the Bond crack theory.

Based on Bond's theory of cracks, the functional relationship between D and Kd is derived, and a prediction criterion for rock drillability indicated by cuttings D is developed, indicating that it is feasible to use the upper returning debris D to describe the drillability.

The fractal method determines the rock drillability grade value with high precision and can be applied as a drillability evaluation method in practice.

However, the grading standards in the text are completely determined by the rock properties of the Songliao Basin. Whether the rock in other oilfields has corresponding precision needs further research.

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