Mathematical Model of the Diamond-Bit Drilling Process and Its Practical Application

1982 ◽  
Vol 22 (06) ◽  
pp. 911-922 ◽  
Author(s):  
Malgorzata B. Ziaja ◽  
Stefan Miska

Abstract With several limiting assumptions, a mathematical model of the diamond-bit drilling, process has been developed. The model represented by an instantaneous rate-of-penetration equation takes into account the reduction in penetration rate during drilling resulting from bit wear. The model has been tested both under laboratory and under field conditions. The comparison of the theoretical and experimental results has shown reasonable agreement. A method for estimating rock properties also has been established. Using this method, we can find the so-called index of rock strength and the index of rock abrasiveness. Introduction Several published studies concerned with diamond-bit drilling report on rock properties and drillability. drilling fluid additives, diamond wear, and drilling performance theories. Among the factors, that affect diamond-bit drilling performance, the type of formation to be drilled is of utmost importance since it significantly affects the type of bit, the drilling practices. and subsequently the rate of penetration and the drilling cost. The nature of the formation is also one of the main factors in planning deep wells, fracture jobs, mud and cement technologies, etc. For rock properties evaluation as well as for selection of proper drilling practices, several descriptions of the diamond-bit drilling process have been developed. The relevant literature is extensive and is not reviewed in this paper. The objective of this paper is to describe the diamondbit drilling model for surface-set diamond core bits and its application to determining the index of formation strength and the index of formation abrasiveness. The main difference between our model and the models known in literature is that we consider the effect of friction between the diamond cutting surfaces and the rock. A decrease in penetration rate is observed if the drilling parameters, are constant and if the formation is macroscopohomogeneous. Drilling Model The drilling model for a surface-set diamond core bit is subjected to the following limiting assumptions.Rock behavior during cutting with a single diamond may be approximated by a rigid Coulomb plastic material.The active surface of the bit is flat, and diamonds are spherical with diameter. d.The cross-sectional area of the chip formed by a single diamond is equal to the diamond cutting surface and can be established by geometry.During drilling, the neighboring diamonds work together to make a uniform depth of cut (Fig. 1).A number of diamonds forming one equivalent blade have to provide it uniform depth of cut from the inner to the outer diameter of the diamond core bit. so the bit is modeled to be a combination of several equivalent blades (Fig. 2).The diamond distribution technique provides uniform radial coverage that results in equally loaded cutting diamonds.Individual cutting diamonds perform some work that results from the friction between the rock and the diamond.Bit wear is assumed to be gradual while drilling is in progress. Under the preceding assumptions we may state that the drilling rate of the surface-set diamond core bit is a function only of weight on bit (WOB), rotary speed, average density of the diamonds on the bit's active surface, diamond size, core-bit diameters, rock properties, and degree of diamond dullness. The effects of flow rate, differential pressure, hydraulic lift, drilling fluid properties. and drillstring dynamics are ignored. According to Peterson, the penetration rate of the diamond bit, after some modifications, can be described by the following simplified equation. (1) This equation does not include the effect of diamond wear and hence pertains to unworn bits or to when bit dullness is negligible. SPEJ P. 911^

1969 ◽  
Vol 9 (03) ◽  
pp. 301-310 ◽  
Author(s):  
D.S. Rowley ◽  
F.C. Appl

Abstract With, the assumption of perfect cleaning, a theory of the drilling performance of surface set diamond bits has been developed. The analysis is based on the previously developed theory of the cutting action of a single diamond, in which it was assumed that rock behavior during cutting may be approximated by that of a rigid-plastic, Coulomb material. With specified drilling conditions and rock formation, expressions for bit torque and bit weight are obtained in terms of bit penetration rate. Expressions also are obtained for the depths of cut of the diamonds. Note that depth of cut and diamond cutting force vary considerably over the cutting surface of the bit. Theoretical results are compared with experimental results for full hole bits and core bits. The agreement is reasonable. Introduction A theoretical analysis of single diamond cutting action on rock has been presented. Equations were established for the stress distribution on the cutting surface of the diamond, for the normal and the tangential cutting forces, and for the chip volume removed by the diamond. These relations were obtained by assuming that the principal, mode of material removal is by "ploughing", and that the rock formation may be approximated by a rigid-plastic, Coulomb material. It is pertinent to consider the drilling performance of a surface set diamond bit, since the over-all performance is determined by the total effect of the individual diamonds on the cutting surface of the bit. A complete analysis of surface set diamond bit performance should take into account the interaction performance should take into account the interaction of the drilling fluid with the mechanics of the cutting action. All material loosened by the diamonds must be carried away by the drilling fluid as it flows between the cutting face of the bit and the rock being cut. The geometry of the clearance between bit and rock is dependent on the diamond catting action as well as the bit geometry. Still there are many factors related to chip generation and removal. that are not understood, and hence, a complete analysis of bit performance including bit hydraulics effects has not been attempted. The present study relates primarily to the mechanics of cutting. It will be assumed that all of the material removed by the diamonds is immediately flushed away by the drilling fluid. The performance of a diamond bit will be determined for conditions of "perfect cleaning". Theoretical results for penetration rate will, therefore, correspond to the upper limit insofar as cleaning is concerned. Using the previous theory of cutting action, one important step remains in order to determine diamond bit performance. The depth of cut of the diamonds must be determined in terms of bit geometry and drilling rate. Most bits have a relatively large number of diamonds spaced rather closely, together. Various spacing patterns are used. However, irregularities in diamond shape and variation due to manufacturing procedures result in deviations that are as large or procedures result in deviations that are as large or larger than the average depth of cut of the individual diamonds. On a new bit it is probable that there are some diamonds that do not cut at all. It seems impractical to attempt to determine the depth of cut of each individual diamond. Statistical treatment of the depth of cut is perhaps the most desirable. Since there is a large number of cutting points, it has been assumed that the performance of the bit as a whole does not depend significantly on the exact nature of the variation in depth of cut and spacing at each radius. We assumed that at any given radius on the bit cutting surface, the diamonds are either randomly spaced or uniformly spaced and that the diamonds along the circumference at any given radius share the work equally. Also, we assume that the drilling conditions and the rock formation remain constant and that steady-state conditions prevail. SPEJ P. 501


Water ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 127
Author(s):  
Gaoli Zhao ◽  
Pavel G. Talalay ◽  
Xiaopeng Fan ◽  
Nan Zhang ◽  
Yunchen Liu ◽  
...  

Hot-water drilling in ice with near-bottom circulation is more advantageous than traditional hot-water drilling with all-over borehole circulation in terms of power consumption and weight. However, the drilling performance of this type of drill has been poorly studied. Initial experiments showed that drilling with single-orifice nozzles did not proceed smoothly. To achieve the best drilling performance, nozzles with different orifice numbers and structures are evaluated in the present study. The testing results show that a single-orifice nozzle with a 3 mm nozzle diameter and a nine-jet nozzle with a forward angle of 35° had the highest rate of penetration (1.7–1.8 m h−1) with 5.6–6.0 kW heating power. However, the nozzles with backward holes ensured a smoother drilling process and a larger borehole, although the rate of penetration was approximately 13% slower. A comparison of the hollow and solid thermal tips showed that under the same experimental conditions, the hollow drill tip had a lower flow rate, higher outlet temperature, and higher rate of penetration. This study provides a prominent reference for drilling performance prediction and drilling technology development of hot-water drilling in ice with near-bottom circulation.


2021 ◽  
Author(s):  
Alexis Koulidis ◽  
Vassilios Kelessidis ◽  
Shehab Ahmed

Abstract Drilling challenging wells requires a combination of drilling analytics and comprehensive simulation to prevent poor drilling performance and avoid drilling issues for the upcoming drilling campaign. This work focuses on the capabilities of a drilling simulator that can simulate the directional drilling process with the use of actual field data for the training of students and professionals. This paper presents the results of simulating both rotating and sliding modes and successfully matching the rate of penetration and the trajectory of an S-type well. Monitored drilling data from the well were used to simulate the drilling process. These included weight on bit, revolutions per minute, flow rate, bit type, inclination and drilling fluid properties. The well was an S-type well with maximum inclination of 16 degrees. There were continuous variations from rotating to sliding mode, and the challenge was approached by classifying drilling data into intervals of 20 feet to obtain an appropriate resolution and efficient simulation. The simulator requires formation strength, pore and fracture pressures, and details of well lithology, thus simulating the actual drilling environment. The uniaxial compressive strength of the rock layer is calculated from p–wave velocity data from an offset field. Rock drillability is finally estimated as a function of the rock properties of the drilled layer, bit type and the values of the drilling parameters. It is then converted to rate of penetration and matched to actual data. Changes in the drilling parameters were followed as per the field data. The simulator reproduces the drilling process in real-time and allows the driller to make instantaneous changes to all drilling parameters. The simulator provides the rate of penetration, torque, standpipe pressure, and trajectory as output. This enables the user to have on-the-fly interference with the drilling process and allows him/her to modify any of the important drilling parameters. Thus, the user can determine the effect of such changes on the effectiveness of drilling, which can lead to effective drilling optimization. Certain intervals were investigated independently to give a more detailed analysis of the simulation outcome. Additional drilling data such as hook load and standpipe pressure were analyzed to determine and evaluate the drilling performance of a particular interval and to consider them in the optimization process. The resulting rate of penetration and well trajectory simulation results show an excellent match with field data. The simulation illustrates the continuous change between rotating and sliding mode as well as the accurate synchronous matching of the rate of penetration and trajectory. The results prove that the simulator is an excellent tool for students and professionals to simulate the drilling process prior to actual drilling of the next inclined well.


2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Ahmad Al-AbdulJabbar ◽  
Salaheldin Elkatatny ◽  
Mohamed Mahmoud ◽  
Khaled Abdelgawad ◽  
Abdulaziz Al-Majed

During the drilling operations, optimizing the rate of penetration (ROP) is very crucial, because it can significantly reduce the overall cost of the drilling process. ROP is defined as the speed at which the drill bit breaks the rock to deepen the hole, and it is measured in units of feet per hour or meters per hour. ROP prediction is very challenging before drilling, because it depends on many parameters that should be optimized. Several models have been developed in the literature to predict ROP. Most of the developed models used drilling parameters such as weight on bit (WOB), pumping rate (Q), and string revolutions per minute (RPM). Few researchers considered the effect of mud properties on ROP by including a small number of actual field measurements. This paper introduces a new robust model to predict the ROP using both drilling parameters (WOB, Q, ROP, torque (T), standpipe pressure (SPP), uniaxial compressive strength (UCS), and mud properties (density and viscosity) using 7000 real-time data measurements. In addition, the relative importance of drilling fluid properties, rock strength, and drilling parameters to ROP is determined. The obtained results showed that the ROP is highly affected by WOB, RPM, T, and horsepower (HP), where the coefficient of determination (T2) was 0.71, 0.87, 0.70, and 0.92 for WOB, RPM, T, and HP, respectively. ROP also showed a strong function of mud fluid properties, where R2 was 0.70 and 0.70 for plastic viscosity (PV) and mud density, respectively. No clear relationship was observed between ROP and yield point (YP) for more than 500 field data points. The new model predicts the ROP with average absolute percentage error (AAPE) of 5% and correlation coefficient (R) of 0.93. In addition, the new model outperformed three existing ROP models. The novelty in this paper is the application of the clustering technique in which the formations are clustered based on their compressive strength range to predict the ROP. Clustering yielded accurate ROP prediction compared to the field ROP.


2011 ◽  
Vol 243-249 ◽  
pp. 3612-3617 ◽  
Author(s):  
Zhan Tao Li ◽  
Ken Ichi Itakura

This paper proposes an analytical model to describe rock drilling processes using drag bits and rotary drills, and to induce relations among rock properties, bit shapes, and drilling parameters (rotary speed, thrust, torque, and stroke). In this model, a drilling process is divided into successive cycles. Each cycle includes two motions: feed and cutting. According to this model, drilling torque includes four components generated from cutting, friction, feed, and idle running respectively, the first three items are all proportional to the uniaxial compressive strength (UCS) when the penetration rate is constant. Laboratory tests verified the correctness and effectiveness of the proposed model qualitatively. Especially, the influence of friction on the flank face and the idle running was confirmed. Field experiments were performed. The results showed good correlation between the torque, penetration rate, and UCS. The proposed model and equations engender the possibility of eliminating useless components of cutting forces when investigating the relation between mechanical data and physical properties of rocks.


2020 ◽  
Vol 177 ◽  
pp. 01008
Author(s):  
Andrey Regotunov ◽  
Rudolf Sukhov ◽  
Gennady Bersenyov

As a system, the mining enterprise develops under constantly changing conditions of the external and internal environment. These conditions affect the state of the most important drilling subsystem: blasthole drilling technology, safety, performance, power consumption of the boring rigs and roller bits used. The main transition processes as necessary responses of the subsystem to changing conditions were identified as a result of fragmentary data analysis showing decisions taken over the past 15-20 years, which increase drilling activity efficiency and safety of smaller quarries of Russia, which contain a significant amount of material resources. The main transition processes contribute to the growth of drilling performance and consist of changing the following: bit design for specific rocks; drilling method; drilling mode; boring rig design; controlled parameters of drilling process and rock properties redetermination; parameters of maintenance and repair system. Based on the performed analysis, the systematization results of the main factors predetermining the need for transition processes implementation in the “drilling operations” subsystem were obtained and presented. The proposed approach allowed to reveal a holistic picture of the main interacting factors in the “drilling operations” subsystem. Based on the factors systematization presented in the article it is possible to envisage changes of individual factors depending on changes of other factors, not functionally related directly when planning drilling operations.


2021 ◽  
Author(s):  
Kingsley Williams Amadi ◽  
Ibiye Iyalla ◽  
Yang Liu ◽  
Mortadha Alsaba ◽  
Durdica Kuten

Abstract Fossil fuel energy dominate the world energy mix and plays a fundamental role in our economy and lifestyle. Drilling of wellbore is the only proven method to extract the hydrocarbon reserves, an operation which is both highly hazardous and capital intensive. To optimize the drilling operations, developing a high fidelity autonomous downhole drilling system that is self-optimizing using real-time drilling parameters and able to precisely predict the optimal rate of penetration is essential. Optimizing the input parameters; surface weight on bit (WOB), and rotary speed (RPM) which in turns improves drilling performance and reduces well delivery cost is not trivial due to the complexity of the non-linear bit-rock interactions and changing formation characteristics. However, application of derived variables shows potential to predict rate of penetration and determine the most influential parameters in a drilling process. In this study the use of derived controllable variables calculated from the drilling inputs parameters were evaluated for potential applicability in predicting penetration rate in autonomous downhole drilling system using the artificial neutral network and compared with predictions of actual input drilling parameters; (WOB, RPM). First, a detailed analysis of actual rock drilling data was performed and applied in understanding the relationship between these derived variables and penetration rate enabling the identification of patterns which predicts the occurrence of phenomena that affects the drilling process. Second, the physical law of conservation of energy using drilling mechanical specific energy (DMSE) defined as energy required to remove a unit volume of rock was applied to measure the efficiency of input energy in the drilling system, in combination with penetration rate per unit revolution and penetration rate per unit weight applied (feed thrust) are used to effective predict optimum penetration rate, enabling an adaptive strategize which optimize drilling rate whilst suppressing stick-slip. The derived controllable variable included mechanical specific energy, depth of cut and feed thrust are calculated from the real- time drilling parameters. Artificial Neutral Networks (ANNs) was used to predict ROP using both input drilling parameters (WOB, RPM) and derived controllable variables (MSE, FET) using same network functionality and model results compared. Results showed that derived controllable variable gave higher prediction accuracy when compared with the model performance assessment criteria commonly used in engineering analysis including the correlation coefficient (R2) and root mean square error (RMSE). The key contribution of this study when compared to the previous researches is that it introduced the concept of derived controllable variables with established relationship with both ROP and stick-slip which has an advantage of optimizing the drilling parameters by predicting optimal penetration rate at reduced stick-slip which is essential in achieving an autonomous drilling system. :


2019 ◽  
Vol 141 (10) ◽  
Author(s):  
A. N. Abugharara ◽  
Bashir Mohamed ◽  
C. Hurich ◽  
J. Molgaard ◽  
S. D. Butt

The influence of shale anisotropy and orientation on shale drilling performance was studied with an instrumented laboratory drilling rig with a 38.1-mm dual-cutter polycrystalline diamond compact (PDC) bit, operating at a nominally fixed rotational speed with a constant rate of flow of drilling fluid—water. However, the rate of rotation (rpm) was affected by the weight on bit (WOB), as was the torque (TRQ) produced. The WOB also affected the depth of cut (DOC). All these variables, WOB, rpm, TRQ, and DOC, were monitored dynamically, for example, rpm with a resolution of one-third of a revolution (samples at time intervals of 0.07 s.) The shale studied was from Newfoundland and was compared with similar tests on granite, also from a local site. Similar tests were also conducted on the concrete made with fine aggregate, used as “rock-like material” (RLM). The shale samples were embedded (laterally confined) in the concrete while drilled in directions perpendicular, parallel, and at 45 deg orientations to bedding planes. Cores were produced from all three materials in several directions for the determination of oriented physical properties derived from ultrasonic testing and oriented unconfined compressive strength (OUCS). In the case of shale, directions were set relative to the bedding. In this study, both primary (or compression) velocity Vp and shear ultrasonic velocity Vs were found to vary with orientation on the local shale samples cored parallel to bedding planes, while Vp and Vs varied, but only slightly, with orientation in tests on granite and RLM. The OUCS data for shale, published elsewhere, support the OUCS theory of this work. The OUCS is high perpendicular and parallel to shale bedding, and is low oblique to shale bedding. Correlations were found between the test parameters determined from the drilling tests on local shale. As expected, ROP, DOC, and TRQ increase with increasing WOB, while there are inverse relationships between ROP, DOC, and TRQ with rpm on the other hand. All these parameters vary with orientation to the bedding plane.


2021 ◽  
Vol 36 (5) ◽  
pp. 141-153
Author(s):  
Hamidreza Saeedi ◽  
Seyed-Mohamad Esmaeil Jalali ◽  
Mehdi Noroozi ◽  
Somayeh Behraftar

One of the criteria in the operational efficiency of drilling is the rate of penetration of the drill bit. Numerous factors affect the rate of penetration. Identification of the effective factors on rate of penetration may lead to a more accurate assessment of drilling time, and as a result, the controlling of operational costs. The concurrent effect of the entire influential factors as well as the differing significance of each of them on the rate of penetration makes the study and optimization of drilling operations much more complicated and difficult. Using the rock engineering systems (RES), the impact of effective operational and geomechanical factors on the rate of penetration has been assessed in this article and a model has been proposed for the prediction of the rate of penetration. Data from one of the wells within the Azadegan oilfield have been used in order to study the impact of effective factors on the rate of penetration. To this end, the effective factors on rate of penetration are initially identified and then an index called “the rate of penetration index (ROPi)” is proposed through the application of the rock engineering systems approach. This index has been calculated at four different depths along the aforementioned well. The results suggested the compliance of penetration rate predictions with field observations. Moreover, porosity and uniaxial compressive strength are the most effective factors on the rate of penetration whereas the weight of drilling fluid has the smallest impact. Finally, a classification for the penetration rate index is presented.


2018 ◽  
Vol 2 (2) ◽  
pp. 3-13
Author(s):  
Maha R. A. Hamoudi ◽  
Akram H. Abdulwahhab ◽  
Amanj Walid Khalid ◽  
Deelan Authman ◽  
Rebin Ali Mohammed Ameen

One of the most important functions performed by drilling fluid is the removal of cutting from the bottom of the hole to the surface. This function must be performed efficiently if not, the cuttings produced during drilling process will accumulate in the annulus. This problem in directional drilling is featured by gravitational forces. Problems resulting from inefficient cutting transport include pipe stuck, wear of bit, reduction in penetration rate, high torque and drag with many other problems encountered. In high angle deviated wells, the cutting goes through a complex path to the surface where some of the cuttings gravitate to the low side of the well. Reduction in any problem associated with improper cutting transport require good understanding in cutting transport mechanisms. This research focuses on calculating the minimum annular velocity of drilling fluid and minimum pump flow rate which is required to achieve hole- cleaning and lifting of the cutting to the surface, taking into consideration the main parameters that affect the coring capacity of the drilling fluid, for this purpose, data of a deviated well (X) located in Kurdistan region of Iraq is collected to determine slip velocity, annular velocity, critical flow rate and carrying capacity index taking in consideration the mud used and the angle of the deviation using the drilling formula spread sheet V1.6.


Sign in / Sign up

Export Citation Format

Share Document