Currently, there is a tendency of constant increase in the number of sticking in directional and horizontal wells as a result of the open hole narrowing caused by the viscoplastic deformation (creep) of rock. The article deals with the problem of elastic-viscoplastic borehole walls displacements of time in an isotropic compressible rock mountain with a uniform lateral pressure. To solve the problem we applied the methods of the theory of elasticity, creep theory and rock mechanics. As a result, the analytical solution of the problem is derived dependence of the increment of axial stress in the compressible isotropic rock. To perform calculations of elastic-viscoplastic borehole walls displacements of inclined and horizontal boreholes in time we developed a computer program in MS Excel environment. The following initial data is entered for the calculation of the program: the diameter of the well, the inclination angle, rock pressure, mud pressure in this section of the interval, the elastic modulus by the die indentation method, the Poisson's ratio, creep coefficients of Abel kernel.

The developed computer program calculated the elastic-viscoplastic borehole walls displacements (necking of borehole) in the formation of rock salt of the Astrakhan gas-condensate field. Pots elastic-viscoplastic borehole walls displacements of directed well in time (for example, range from inclination angle 300) and elastic-viscoplastic borehole walls displacements dependence on the inclination angle (ceteris paribus) were obtained. In the first 2 h of movement of the upper borehole wall increases linearly in time, which mainly characterizes the elastic deformation of the rock stage. Further displacement of the borehole wall increases nonlinearly, i.e. there is a viscoplastic deformation of the rock. Elastic-viscoplastic displacement of the upper wall of the borehole at module is significantly (more than in 5 times) greater than elastic-viscoplastic displacement of the side wall of the well at a time. So that the cross-section of the wells open hole becomes elliptical. With increasing the inclination angle elastic-viscoplastic displacement of the top wall increases continuously while elastic-viscoplastic displacement on the side wall decreases to zero with increasing the inclination angle 250 and then increasing the inclination angle 250 is increased with a positive value.

The research results can be applied to predict and prevent sticking of the drill string for oil and gas wells drilling.

References

1. Popov A.N., Moguchev A.I., Popov M.A., Deformation of walls of an inclined well and its influence on work and wear of drilling bits (In Russ.), Stroitel’stvo neftyanykh i gazovykh skvazhin na sushe i na more, 2008, no. 3, pp. 6–13.

2. Popov A.N., Moguchev A.I., Popov M.A., Harmonization of hardness scales of rocks with indicators of their mechanical properties (In Russ.), Stroitel’stvo neftyanykh i gazovykh skvazhin na sushe i na more, 2009, no. 2, pp. 18–23.

3. Gubaydullin A.G., Moguchev A.I., Directional hole shifts under tectonic stress (In Russ.), Gazovaya promyshlennost’ = GAS Industry of Russia, 2015, no. 12, pp. 88-91.

4. Moguchev A.I., Gubaydullin A.G., Lobankov V.M., Belyaeva A.S., Effect of rock fracturing on elastoviscoplastic displacement of borehole walls (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2016, no. 5, pp. 41–43.

5. Gubaydullin A.G., Moguchev A.I., Elastoviscoplastic displacement of wellbore walls in deviated and horizontal wellbores (In Russ.), Territoriya Neftegaz, 2016, no. 3, pp. 48-55.

6. Popov A.N., Specification of the calculation of elastic stress components in a vertical well (In Russ.), Izvestiya vuzov. Neft’ i gaz, 1990, no. 3, pp. 21–24.

7. Metodika rascheta uprugogo smeshcheniya stenok skvazhiny posle vskrytiya gornoy porody bureniem (The methodology of calculation of the elastic displacement of the borehole walls after completion), Draftsmen: Popov A.N., Bulyukova F.Z., Moguchev A.I., Krysin N.I., Ufa: Publ. of USPTU, 2011, 24 p.

8. Rabotnov A.N., Elementy nasledstvennoy mekhaniki deformiruemykh tverdykh tel (Elements of hereditary mechanics of deformed solids in a vertical well), Moscow: Nauka Publ., 1978, 384 p.

9. Erzhanov Zh.S., Teoriya polzuchesti gornykh porod i ee prilozheniya (The theory of rock creep and its applications), Alma-Ata: Nauka Publ., 1964, 173 p.

10. Erzhanov, Zh.S., Karimbaev T.D., Metod konechnykh elementov v zadachakh mekhaniki gornykh porod (The finite element method in problems of rock mechanics), Alma-Ata: Nauka Publ., 1975, 241 p.

11. Kashnikov Yu.A., Ashikhmin S.G., Mekhanika gornykh porod pri razrabotke mestorozhdeniy uglevodorodnogo syr’ya (Rock mechanics in the development of hydrocarbon fields), Moscow: Nedra – Biznes-tsentr Publ., 2007, 476 p.Currently, there is a tendency of constant increase in the number of sticking in directional and horizontal wells as a result of the open hole narrowing caused by the viscoplastic deformation (creep) of rock. The article deals with the problem of elastic-viscoplastic borehole walls displacements of time in an isotropic compressible rock mountain with a uniform lateral pressure. To solve the problem we applied the methods of the theory of elasticity, creep theory and rock mechanics. As a result, the analytical solution of the problem is derived dependence of the increment of axial stress in the compressible isotropic rock. To perform calculations of elastic-viscoplastic borehole walls displacements of inclined and horizontal boreholes in time we developed a computer program in MS Excel environment. The following initial data is entered for the calculation of the program: the diameter of the well, the inclination angle, rock pressure, mud pressure in this section of the interval, the elastic modulus by the die indentation method, the Poisson's ratio, creep coefficients of Abel kernel.

The developed computer program calculated the elastic-viscoplastic borehole walls displacements (necking of borehole) in the formation of rock salt of the Astrakhan gas-condensate field. Pots elastic-viscoplastic borehole walls displacements of directed well in time (for example, range from inclination angle 300) and elastic-viscoplastic borehole walls displacements dependence on the inclination angle (ceteris paribus) were obtained. In the first 2 h of movement of the upper borehole wall increases linearly in time, which mainly characterizes the elastic deformation of the rock stage. Further displacement of the borehole wall increases nonlinearly, i.e. there is a viscoplastic deformation of the rock. Elastic-viscoplastic displacement of the upper wall of the borehole at module is significantly (more than in 5 times) greater than elastic-viscoplastic displacement of the side wall of the well at a time. So that the cross-section of the wells open hole becomes elliptical. With increasing the inclination angle elastic-viscoplastic displacement of the top wall increases continuously while elastic-viscoplastic displacement on the side wall decreases to zero with increasing the inclination angle 250 and then increasing the inclination angle 250 is increased with a positive value.

The research results can be applied to predict and prevent sticking of the drill string for oil and gas wells drilling.

References

1. Popov A.N., Moguchev A.I., Popov M.A., Deformation of walls of an inclined well and its influence on work and wear of drilling bits (In Russ.), Stroitel’stvo neftyanykh i gazovykh skvazhin na sushe i na more, 2008, no. 3, pp. 6–13.

2. Popov A.N., Moguchev A.I., Popov M.A., Harmonization of hardness scales of rocks with indicators of their mechanical properties (In Russ.), Stroitel’stvo neftyanykh i gazovykh skvazhin na sushe i na more, 2009, no. 2, pp. 18–23.

3. Gubaydullin A.G., Moguchev A.I., Directional hole shifts under tectonic stress (In Russ.), Gazovaya promyshlennost’ = GAS Industry of Russia, 2015, no. 12, pp. 88-91.

4. Moguchev A.I., Gubaydullin A.G., Lobankov V.M., Belyaeva A.S., Effect of rock fracturing on elastoviscoplastic displacement of borehole walls (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2016, no. 5, pp. 41–43.

5. Gubaydullin A.G., Moguchev A.I., Elastoviscoplastic displacement of wellbore walls in deviated and horizontal wellbores (In Russ.), Territoriya Neftegaz, 2016, no. 3, pp. 48-55.

6. Popov A.N., Specification of the calculation of elastic stress components in a vertical well (In Russ.), Izvestiya vuzov. Neft’ i gaz, 1990, no. 3, pp. 21–24.

7. Metodika rascheta uprugogo smeshcheniya stenok skvazhiny posle vskrytiya gornoy porody bureniem (The methodology of calculation of the elastic displacement of the borehole walls after completion), Draftsmen: Popov A.N., Bulyukova F.Z., Moguchev A.I., Krysin N.I., Ufa: Publ. of USPTU, 2011, 24 p.

8. Rabotnov A.N., Elementy nasledstvennoy mekhaniki deformiruemykh tverdykh tel (Elements of hereditary mechanics of deformed solids in a vertical well), Moscow: Nauka Publ., 1978, 384 p.

9. Erzhanov Zh.S., Teoriya polzuchesti gornykh porod i ee prilozheniya (The theory of rock creep and its applications), Alma-Ata: Nauka Publ., 1964, 173 p.

10. Erzhanov, Zh.S., Karimbaev T.D., Metod konechnykh elementov v zadachakh mekhaniki gornykh porod (The finite element method in problems of rock mechanics), Alma-Ata: Nauka Publ., 1975, 241 p.

11. Kashnikov Yu.A., Ashikhmin S.G., Mekhanika gornykh porod pri razrabotke mestorozhdeniy uglevodorodnogo syr’ya (Rock mechanics in the development of hydrocarbon fields), Moscow: Nedra – Biznes-tsentr Publ., 2007, 476 p.