MODELLING OF HORIZONTAL DRILL STRING MOTION BY THE LUMPED-PARAMETER METHOD
DOI:
https://doi.org/10.26577/JMMCS.2022.v115.i3.012Keywords:
drill string, nonlinear, vibrations, lumped-parameter method, parallel programmingAbstract
The motion of drill strings is modeled in the drilling of geotechnological wells in the mining industry by the Lumped-Parameter Method (LPM). This method is widely used in structural mechanics and is most justified in modeling dynamic systems with a variable structure. On the example of horizontal drilling of geotechnological wells, longitudinal vibrations of a drill string with a static compressive load at the left end are considered [1]. The contact interaction of the drill string with the borehole walls and the inertia force of the bit on the destructible rock at the right end of the string are taken into account. The analysis of the column splits number, which specifies the dimension of the system of discrete equations, is carried out by verifying the obtained results with the previously known data [1]. For verification, the developed C# software was used, allowed to determine the error of the column splits in comparison with the test data. The optimal number of the drill string splits in terms of "implementation time - calculation error" by the LPM was identified. The numerical implementation of the model is conducted by the fourth-order Runge-Kutta method. In connection with the increase in the implementation time of the program code due to the increase in the dimension of the system, the numerical algorithm is optimized using the parallel programming tools. The expediency of this optimization is analyzed.
References
[2] International Association of Drilling Contractors IADC Drilling Manual, (USA: Technical Toolboxes Inc, 2000).
[3] Basarygin Yu.M., Bulatov A.I., Proselkov Yu.M. (2002) Burenie neftianykh i gazovykh skvazhin [Drilling of oil and gas wells] (M.:Nedra-Biznescentr)
[4] Willoughby D.A., Horisontal directional drilling, (USA: The McGraw-Hill Companies Inc, 2005).
[5] Ritto T.G., Sampaio R., “Stochastic drill-string dynamics with uncertainty on the imposed speed and on the bit-rock parameters”, Int. J. Uncertain. Quantification. 2(2) (2012): 111-124.
[6] Lobo D.M., Ritto T.G., Castello D.A., “Stochastic analysis of torsional drill-string vibrations considering the passage from a soft to a harder rock layer”, J. Braz. Soc. Mech. Sci. Eng. 39(6) (2017): 2341-2349.
[7] Jialin T., Yinglin Ya., Lin Ya., “Vibration characteristics analysis and experimental study of horizontal drill string with wellbore random friction force”, Arch. Appl. Mech. 87 (2017): 1439-1451.
[8] Zhanghua L., Qiang Zh., Tiejun L., Fuhui W., “Experimental and numerical study of drill string dynamics in gas drilling of horizontal wells”, J. Nat. Gas Sci. Eng. 27 (2015): 1412-1420.
[9] Tiejun L., Qiang Zh., Zhanghua L., Zhou X., Tao W. , Gao Li., Jiandong D., “Experimental study on vibrational behaviors of horizontal drillstring”, J. Pet. Sci. Eng. 164 (2018): 311-319.
[10] Kh.A. Sarsenbayev, B.S. Khamzina, G.A. Koldassova, G.B. Issayeva (2017) Primenenie biopolimernykh rastvorov dlia effektivnogo vskrytiia produktivnykh gorizontov gorizontalnykh skvazhin [Application of biopolymer drilling fluid for effective opening productive horizons horisontal wells]. News of the National Academy of Sciences of the Republic of Kazakhstan, Series Physico-mathematical, vol. 312, no. 2, pp. 161-165.
[11] Salehi M.M., Moradi H., Nonlinear multivariable modeling and stability analysis of vibrations in horizontal drill string”, Appl. Math. Model. 71 (2019): 525-542.
[12] Yiwei H., Zhijiu A., YuchunK., Jianxun L., Wenwu Ya., “Nonlinear dynamic modeling of drill string in horizontal well -A geometrically exact approach”, J. Pet. Sci. Eng. 172 (2019): 1133-1152.
[13] Sadler J.P., A lumped parameter approach to the kineto-elastodynamic analysis of mechanisms ( USA: Rensselaer Polytechn. Institute, 1971)
[14] Sadler J.P., Sandor G.N., “A Lumped parameter approach to vibration and stress analysis of elastic linkages” , J. Eng. Ind. 95(2) (1973): 549-557.
[15] Sadler J.P., Sandor G.N., “Nonlinear vibration analysis of elastic four-bar linkages”, J. Eng. Ind. 96(2) (1974): 411-419.
[16] Sadler J.P., “On the Analytical Lumped-Mass Model of an Elastic Four-Bar Mechanism”, J. Eng. Ind. 97(2) (1975): 561-565.
[17] Wang Y., Huston R.L., “A lumped parameter method in the nonlinear analysis of flexible multibody systems”, Comput. Struct. 20(3) (1994): 421-432.
[18] Salinic S., Nikolic A., “On the free vibration of a multiplestepped cantilever beam”, Fourth Serbian (29th Yu) Congress on Theoretical and Applied Mechanics, Serbia, 4-7 June 2013.
[19] Giorgio I., Dionisio D.V., “Non-linear lumped-parameter modeling of planar multi-link manipulators with highly flexible arms”, Robotics 7(4) (2018): 60.
[20] Khajiyeva L., Sergaliyev A., “About discretization of the horizontal drill-string model with uncertainty on the frictional force by the lumped parameters method”, Appl. Mech. Mater. 665 (2014): 589-592.
