The research on calculation of torque and drag in highly deviated wells has demonstrated a significant gap against oil exploration and development; with the increasingly rigorous situation, the drill string dynamics and the contact or friction of drill pipe with borehole wall under the drill string action of dynamic need more attention and urgent research work. Based on full-hole system dynamics, three-dimensional nonlinear dynamic model and dynamic torque and drag model were established in highly deviated well by using the finite element method. An application of analyzing typical torque and drag problems presented here provides a means to more accurate description of the contact relation between drill string and wellbore. The results show that those models established in this paper have complete adaptability for a complex three-dimensional borehole trajectory. For the actual well application, it will help to evaluate security performance of drill string in complex working conditions.
With scarcity of resources, great difficulties have been confronted with oil companies during the process of exploration drilling of oil or gas and the complexity of drilling geological environment is now bottlenecking the development of drilling technology. Due to the geographical conditions, most oil and gas wellbore trajectories have to be catenary curve which is used to substitute for straight line; well profiles have to adopt highly deviated well [
In brief, the above-mentioned problems commonly exist in highly deviated wells; on the basis of torque and drag modeling originally started by the works of Johancsik et al. [
Overall, the research on calculation of torque and drag should be deeper and wider in highly deviated wells, resulting in a lot of errors in the torque and drag parameters computed, which has demonstrated a significant gap against oil exploration and development with the increasingly rigorous situation, so the drill string dynamics and the contact or friction of drill pipe with borehole wall under the drill string action of dynamic need more attention and urgent research work, its purposes are to study the drill string vibration rules and the reasons of drill string failure in highly deviated wells, especially to understand the law of torque and drag and promote the development of new drilling technologies in special technology. Therefore, this paper established the models for vertical, lateral, and torsion coupled vibration of full-hole drilling strings in highly deviated well with mud drilling using the finite element method to dynamically analyze torque and drag of string drilling in operation.
The new model has been developed based on full-hole system dynamics, in which the finite element method is used to model the drill string used in rotational drilling operations. The ABAQUS FEM Explicit solver package was used to develop the dynamic FEM model [
Before establishing the model, the following main assumptions would be needed with synthesizing structure characteristics of full-hole drilling strings, boundary constrains, and load conditions, based on the theory of nonlinear transient: the drill string is simplified to homogeneous beam; cross section shape is circle, ignoring threaded connections between the drill string and partially perforated structures; the geometric size of the drill string and material properties of the drill string can be segmented or grouped depending on drilling tools assembly without considering the impact of temperature; keep the rotation speed constant at the top of the drill string; rock fragmentation process in real time is used for the boundary condition of the end of the drill string, because strength and hardness of bit is greater than that of bottom rock, so set bit to a rigid body in the analysis; rock is assumed to be an isotropic material and rock nonlinearity is simulated by DP elastic-plastic model; simply using finite element method removes the failure elements from rock elements and ignores its influence on subsequent drilling; borehole wall has large rigidity; its cross section is usually in a circular form; its axis is a smooth curve in three-dimensional space with continuous second order derivatives which was made as interpolation to the measured well inclination data.
Accordingly, one needs to write the kinetic and strain energy expressions. In this context, the kinetic energy can be expressed in the form as [
The total strain energy can be written in compact matrix form as
Based on the Hamilton theory [
The following boundary conditions are considered. As a result of the limitation of wheel to drill string in well hole, wellhead node lateral displacement and lateral rotation angle are zero, correcting wellhead node generalized displacement in real time, keeping lateral force the same. Twisting vibration is thought to exist when dealing with the drill string twist boundary, but only mainly in lower parts of drill string. For the top node of the drill string, because of the constant power drilling rig, we assume that rotating speed of the top node is constant, but its torque is fluctuating. Axial displacement of the top node is not fixed, and a lift force is joined on it to simulate the hook load:
Based on the interaction of bit and formation, the force from the rock and bit is used for the boundary condition of the end of the drill string. Considering the coupled relations between the drill string and the bit, both of them are linked into a whole unit to make rock failure and drilling hole without constraints of any degrees of freedom. The formation of the hole is relative to the lower longitudinal vibration of drill string and interaction between bit and formation. The drill bit is a direct tool for rock breakage; the longitudinal impact allows it into the bottom hole rock layer and small pieces of the rock that deform and break away due to the lateral scraping action of the bit teeth. Then cuttings are washed from the bottom by drilling fluid.
Rotating drill string movement along the cross section of the wellbore is hedged about with wellbore wall, when the outer wall of the drill string is closing to borehole wall, and the drill string has a trend of move outwards; then the drill string will collide with the wall with rubbing contact. The contact and friction of a drill pipe string with borehole wall have become the basic research of the drill string dynamics and drag and torque calculation, whose effect on the dynamic characteristics of drill string cannot be ignored, and it is difficult to analyze.
The contact between drill string and borehole wall in the process of highly deviated well drilling is of large area and geometrically nonlinear with unpredictability; this can be seen from the following: inability to forecast the points of contact between borehole wall and drill string, influenced by torsional vibration and axial vibration of drill string, and the value of the impact force and the contact time along the contact position. Even with using the same drilling assembly, the contact position and the value of the contact force are also not the same under different real well trajectory or drilling conditions. So this paper introduces stochastic boundary method for prediction of contact stress.
The annular tolerance between drill string and borehole wall can be used to judge whether the drill string and borehole wall contact in a calculation. Drill string is in a state of freedom of movement without contacting the borehole wall; there is no constraint reaction force. When the drill string connects with borehole wall as shown in Figure
Drill pipe-wellbore contact model: (a) the contact between drill string and borehole wall and (b) the contact interface formed by the drill string and borehole wall.
Set resistance coefficient between drill string and borehole wall
The normal contact force model presented here is different from the models of the studies [
The forces imposed on pipe include the weight of the drill string in air; axial tension of landing by rig, torque, and friction force exists between drill stem and wall; buoyancy effect occurs when the drilling string is submerged in drilling fluid, viscous friction torque, and so on.
Taking the drill string element “ direction is
where
The forces acting on the drill string element.
When the element satisfies
Then, synthesizing friction torque and active torque, we can get the equation for torque of a node:
The above equations of drag and torque are the core content of full well system dynamics modeling. By using mechanics parameters such as velocity and acceleration of drill element node based on
As is apparent from the above model, what makes these equations different between most of the industry widely used torque and drag models based on the soft string model or often called a “cable” or “chain” is that it no longer assumes that the drill string is deformed to the shape of wellbore and has continuous surface contact area between the drill string and borehole but introduces stochastic boundary method for prediction of contact stress. The relations between the drill string and borehole can be contact states, as well as discrete state; at the same time considerations regarding the effects of drill pipe movement could also have been implemented in the present model. In the complex wellbore profiles with micro- and macrotortuosities, the soft string model may introduce errors and cause misinterpretation of drilling problems. Along with this, when the drill string position relative to the wellbore is on the high side, the soft string model cannot predict this situation which in some cases will lead to errors in torque and drag prediction; it excludes the influence on it, but, for this model,
Based on dynamic drag and torque model in highly deviated well, a dynamics model for describing rotary drill in drilling of highly deviated well from Jidong Oilfield in China was established; it considered the drill string-borehole-drill bit-rock as the “drill string vibration system.” In this paper, the system vibration of the drill string is simplified to a high dimensional multidegree of freedom system to analyze with appropriate load and boundary conditions those determined by the construction parameters. The nonlinear mass-spring-damper mechanical system has been used to replace drill string in highly deviated well for analysis drag and torque considering drill string service environment and friction collision between drill string and borehole of drill string and the buoyancy of the mud, and so on. The three-dimensional finite-element model was developed using a finite element preprocessor module of ABAQUS; drill string, borehole, drill bit, and rock were modeled by spatial two nodes beam element BEAM31, rigid body shell element R3D4, rigid body shell element R3D4, and three-dimension solid element C3D8R, respectively, by the meshing techniques. The numerical model should look like that shown in Figure
The drill string system numerical model.
Calculation of one of Jidong Oilfield highly deviated wells is by applying this theoretical model and torque and drag analysis. The drilling structure of fourth drilling section is Φ215.9 mm bit × 0.34 m + Φ172 mm screw × 7.69 m + Φ165 check valve × 0.50 m + F206 × 1.53 m + Φ165 Drill collar × 9.09 m + MWD × 2.17 m + Φ165 Drill collar × 9.47 m + Φ139.7 heavy weight drill pipe × 84.53 m (9 drill pipes) + Φ178 drilling jar × 3.57 m + Φ139.7 heavy weight drill pipe × 84.53 m (9 drill pipes) + 139.7 drill pipe + cock + Kelly.
In practical modeling, according to the measured borehole trajectory parameters established drill pipe and borehole, the well depth is 4305 m, the actual well path is as shown in Figure
3D actual wellbore path of NP13-X1042.
Angle of deviation and overall angle change rate.
The damping behavior is considered as Rayleigh damping (a quadratic expression for the energy dissipation rate), which is proportional to the mass and stiffness of each mode. Time increments should be defined properly to achieve efficient computation and capture dynamics in the highest frequency range of interest. The stability limit dictates the maximum time increment used by ABAQUS Explicit. The stability limit will be defined based on the element length and the wave speed inside the material (
Parameters used in the simulations.
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Poisson’s ratio of the wall rock | WOB = 6 | Weight on bit (ton) |
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Poisson’s ratio of the drill string |
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Angular velocity (rad/s) |
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Elastic modulus of the rock (N/m2) |
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Drill string density (kg/m3) |
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Elastic modulus of the drill string (N/m2) |
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Shear modulus (N/m2) |
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Resistance coefficient (N/m) |
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Sliding friction coefficient |
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Damping coefficient (N·s/m) |
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Tangential friction coefficient |
Figure
Distribution of contact force on length for 0~1200 m drill string for highly deviated well at different times.
Distribution of contact force on length for 0~4305 m drill string for highly deviated well at different times.
When the contact force is positive, it is pointing downward and this case illustrates that these drill string nodes contact the wellbore at the high side due to the pull forces; if the direction of the contact force acting on the node is going upwards, this means the contact force is negative and these nodes contact the wellbore at the low side under the influence of gravity. When the bit depth is 1200 m, the cut-off point is found roughly halfway in the build-up section, but, for 4305 m, the location of cut-off point is not the same,; instead, it is found in tail of build-up section. The contact between drill string and borehole wall is only expected to grow as the well depth.
Dynamic drag and torque model in highly deviated well can be visual display of the contact state between drill string and borehole wall and numerical results of the contact force and friction force. The frequent impact may result in the drill string wear and leakage, so the distribution of contact force on length for drill string can predict the wear location of the drill string and guide tools installation which can reduce friction force and friction torque.
It can be known from the analysis of the contact between drill string and borehole wall, in most cases, that drill string contacts the wellbore at the low side under the influence of gravity in angle maintaining interval. However, the situation is not simpler in build-up section; drill string can contact the wellbore at either low side or high side for the pulling effect of drill string in both vertical section and angle maintaining interval. Figure
Distribution of cut-off point for well depth at different times.
By computations and analysis, it is found that distribution of cut-off point associates with the ratio between the length of the nonvertical section and the total length of build-up section of hole. Suppose the ratio equals
Calculation of cut-off point position will help to determine the damage or failure position of casing in drilling operation. Wear position of casing generally occurs in the high side of casing.
Figure
Contact force: (a) transient processes of contact force in the node located at 600 m for 4305 m drill string and (b) transient processes of contact force in the node located at 3000 m for 4305 m drill string.
Figure
Calculated hook loads for well depth at different friction factors.
Figure
Friction force: (a) calculated axial friction force for well depth at different friction factors and (b) calculated standard deviation of axial friction force for well depth at different friction factors.
Figure
Figure
Friction torque: (a) calculated friction torque for well depth at different friction factors and (b) calculated standard deviation of friction torque for well depth at different friction factors.
Figure
Figure
Calculated maximum static of friction torque for well depth at different friction factors.
Throughout the drag and torque analysis, the friction torque and axial friction force both increase with the increase of the well depth, but, for the axial friction force in highly deviated well, no matter how much the axial frictional force is, the value will not get bigger than the total weight of the drill string; that is to say, there will always be a part of drill string weight to provide the downward force needed for the bits to efficiently break rock. Instead, maximum static of friction torque will be more than the rated torque of drilling equipment as the increasing of the well depth, so the maximum static of friction torque is the key factor to determine extension ability in highly deviated well.
Based on nonlinear coupling vibration of drilling string, three-dimensional nonlinear dynamic model and dynamic friction torque model were established in highly deviated well with mud drilling by using the finite element method to study the vibration rule of dynamic drag and friction torque of the drill string in rotary drilling. Dynamic drag and torque model established in this paper has a good adaptability under a complex three-dimensional borehole trajectory in highly deviated well for real drilling; it has much less assumptions and its result is highly coincident with the actual drilling operations. In the process of calculating, continuous distribution of contact no longer has been used for assuming the contact relation of drill string and wellbore; stochastic boundary method was introduced for the prediction of contact stress. This mode can give three-dimensional distribution of the contact for drill string and drill string node. It shows that the drill string of build-up section and those under axial compression are the part of whole well in most fierce collision and the nodes contact state are mainly divided into clearance contact and continuous contact. With the calculation, a cut-off point is found in drill string; it divides the contact state into high side borehole contact and low side borehole contact, and distribution of the cut-off point position is roughly three ladder-like curves along with the oil well depth increasing associated with the ratio between the length of the nonvertical section and the total length of build-up section of hole; when the ratio equals 1-2, the cut-off point position is basically near the halfway point of build-up section; when the ratio is more than 3, the drill string is completely affixed to the high side of borehole in build-up section. Compared to the analytic solution using differential form, this method is available for solving the drill string contact which side of borehole, and this model can be employed for dynamics study; more importantly it makes the results more accessible and acceptable. Dynamic drag and torque model can predict hook load in different drilling sections and the change trend of the hook load along the well depth. When the axial friction force of drill string is less than 2 t, the hook load is not affected by the influence of friction factor; when the axial friction force is greater than 2 tons, different rules are shown in calculated hook load along with the change of drilling sections and the change of the friction factor, and the change of the drill assembly will bring hook load a step change trend. The axial friction force and its average wave amplitude increase with increase of friction factor and well depth. Dynamic drag and torque model has the superiority compared with other analytical methods during the analysis of torque, which can get the friction torque, the standard deviation of friction torque, and the maximum static friction torque. Friction torque and maximum static friction torque basically have a linearly increased trend along with well depth, and added value of friction torque is reducing in the process of friction factor changes from small to big in the same well depth. Drilling section and the drill assembly have great influence on the standard deviation of friction torque. Compared with the axial friction, maximum static friction torque is mainly limitation for extending into ability of highly deviated well.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work reported in this paper was supported by the National Oil & Gas Key Project (2011ZX05050), Natural Science Foundation of China (51222406), New Century Excellent Talents in University of China (NCET-12-1061), Scientific Research Innovation Team Project of Sichuan colleges and universities (12TD007), and the Sichuan Youth Sci-tech Innovation Research Team of Drilling Acceleration (2014TD0025).