Numerous analytical equations obtained to determine the flow of fluid in horizontal wells demonstrate low reliability and complexity of practical use. This article is devoted to the substantiation of the application of probabilistic and statistical methods in the study of fluid flow in such wells. For research, we used the accumulated operating experience of wells at the Tournaisian-Famennian producing object of the Shershnevskoye field, including data on flow rates and geological and technological parameters that probably affect the values of these flow rates (reservoir, bottomhole and annular pressures, effective oil-saturated thickness, permeability and piezoconductivity, skin factor, as well as the length of the horizontal section of the well). Filtration parameters were determined during the interpretation of pressure recovery curves, and three methods were used: graphoanalytical methods taking into account (Yu.P. Borisov) and without taking into account (tangent) after-flow, and also based on the analysis of the pressure derivative in the logarithmic coordinates (Saphir). The purpose of this interpretation approach is to substantiate the most reliable of the three, in fact, indirect methods for determining filtration parameters in the absence of direct measurements. As a result of a detailed statistical analysis, differences were established in the laws of formation of well production rates horizontal wellbore at the Shershnevskoye field in their various ranges. Next, multidimensional mathematical models have been developed that make it possible to determine the flow rates of wells in the considered conditions by the set of geological and technical indicators used as initial data. The reliability of the models is confirmed by statistical parameters and the high convergence of the calculated and actual flow rates. An analysis of the developed models made it possible to establish patterns of production rates that are individual for the conditions under consideration. The main factor controlling the productivity of relatively high- productive wells is reservoir pressure; conditionally low rate - the length of the horizontal section of the trunk. The creation of multidimensional mathematical models for determining production rates made it possible to solve such an urgent problem as choosing the most reliable of the three indirect methods for determining the filtration parameters of the reservoir.

References

1. Zaytsev R.A., Martyushev D.A., Operating experience with a horizontal wells in various geological and physical conditions (for example Perm edge fields) (In Russ.), Burenie i neft', 2019, no. 5, pp. 42–46.

2. Shumilov A.V., Kostitsyn V.I., Savich A.D. et al., Logging techniques for horizontal wells under drilling and operation (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2018, no. 2, pp. 48–52.

3. Savich A.D., Chernykh I.A., Shumilov A.V., Efficiency upgrading of geophysical researches in horizontal wells (In Russ.), Geofizika, 2011, no. 5, pp. 70–80.

4. Borisov Yu.P., Pilatovskiy V.P., Tabakov V.P., Razrabotka neftyanykh mestorozhdeniy gorizontal'nymi i mnogozaboynymi skvazhinami (Oil field development using horizontal and multilateral wells), Moscow: Nedra Publ., 1964, 154 p.

5. Joshi S.D., Augmentation of well productivity with slant and horizontal wells, SPE-15375-PA, 1988.

6. Renard G., Dupuy J.M., Formation damage effects on horizontalwell flow efficiency, SPE-19414-PA, 1991.

7. Nasybullin A.V., Lifant'ev A.V., Vasil'ev V.V., Astakhova A.N., Controlling over the model of liquid stable inflow towards a horizontal well and a crack of endless conductivity (In Russ.), Avtomatizatsiya, telemekhanizatsiya i svyaz' v neftyanoy promyshlennosti, 2014, no. 6, pp. 27–32.

8. Khasanov M.M., Mel'chaeva O.Yu., Roshchektaev A.P., Ushmaev O.S., Steady-state flow rate of horizontal wells in a line drive pattern (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2015, no. 1, pp. 48–51.

9. Galkin V.I., Ponomareva I.N., Chernykh I.A. et al., Methodology for estimating downhole pressure using multivariate model (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2019, no. 1, pp. 40–43.

10. Galkin V.I., Ponomareva I.N., Repina V.A., Study of oil recovery from reservoirs of different void types with use of multidimensional statistical analysis (In Russ.), Vestnik Permskogo natsional'nogo issledovatel'skogo politekhnicheskogo universiteta. Geologiya. Neftegazovoe i gornoe delo = Perm Journal of Petroleum and Mining Engineering, 2016, V. 15, no. 19, pp. 145–154, DOI: 10.15593/2224-9923/2016.19.5.

11. Galkin V.I., Ponomareva I.N., Koltyrin A.N., Development of probabilistic and statistical models for evaluation of the effectiveness of proppant hydraulic fracturing (on example of the Tl-Bb reservoir of the Batyrbayskoe field) (In Russ.), Vestnik Permskogo natsionalʹnogo issledovatelʹskogo politekhnicheskogo universiteta. Geologiya. Neftegazovoe i gornoe delo = Perm Journal of Petroleum and Mining Engineering, 2018, V. 17, no. 1, pp. 37–49, DOI: 10.15593/2224-9923/2018.1.4

12. Martyushev D.A., Ponomareva I.N., Researching features of development of fractured porous reservoirs reserves using well-test data (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2017, no. 10, pp. 102–104.

13. Ponomareva I.N., Martyushev D.A., Akhmetova M.I., Evaluation of the optimal duration of the hydrodynamic studies of low-productivity wells on the example of Ozernoye field (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2016, no. 1, pp. 60–63.

14. Ponomareva I.N., Martyushev D.A., Estimating reliability of reservoir properties determination on the basis of production analysis and pressure stabilization curves (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2019, no. 8, pp. 111–113.Numerous analytical equations obtained to determine the flow of fluid in horizontal wells demonstrate low reliability and complexity of practical use. This article is devoted to the substantiation of the application of probabilistic and statistical methods in the study of fluid flow in such wells. For research, we used the accumulated operating experience of wells at the Tournaisian-Famennian producing object of the Shershnevskoye field, including data on flow rates and geological and technological parameters that probably affect the values of these flow rates (reservoir, bottomhole and annular pressures, effective oil-saturated thickness, permeability and piezoconductivity, skin factor, as well as the length of the horizontal section of the well). Filtration parameters were determined during the interpretation of pressure recovery curves, and three methods were used: graphoanalytical methods taking into account (Yu.P. Borisov) and without taking into account (tangent) after-flow, and also based on the analysis of the pressure derivative in the logarithmic coordinates (Saphir). The purpose of this interpretation approach is to substantiate the most reliable of the three, in fact, indirect methods for determining filtration parameters in the absence of direct measurements. As a result of a detailed statistical analysis, differences were established in the laws of formation of well production rates horizontal wellbore at the Shershnevskoye field in their various ranges. Next, multidimensional mathematical models have been developed that make it possible to determine the flow rates of wells in the considered conditions by the set of geological and technical indicators used as initial data. The reliability of the models is confirmed by statistical parameters and the high convergence of the calculated and actual flow rates. An analysis of the developed models made it possible to establish patterns of production rates that are individual for the conditions under consideration. The main factor controlling the productivity of relatively high- productive wells is reservoir pressure; conditionally low rate - the length of the horizontal section of the trunk. The creation of multidimensional mathematical models for determining production rates made it possible to solve such an urgent problem as choosing the most reliable of the three indirect methods for determining the filtration parameters of the reservoir.

References

1. Zaytsev R.A., Martyushev D.A., Operating experience with a horizontal wells in various geological and physical conditions (for example Perm edge fields) (In Russ.), Burenie i neft', 2019, no. 5, pp. 42–46.

2. Shumilov A.V., Kostitsyn V.I., Savich A.D. et al., Logging techniques for horizontal wells under drilling and operation (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2018, no. 2, pp. 48–52.

3. Savich A.D., Chernykh I.A., Shumilov A.V., Efficiency upgrading of geophysical researches in horizontal wells (In Russ.), Geofizika, 2011, no. 5, pp. 70–80.

4. Borisov Yu.P., Pilatovskiy V.P., Tabakov V.P., Razrabotka neftyanykh mestorozhdeniy gorizontal'nymi i mnogozaboynymi skvazhinami (Oil field development using horizontal and multilateral wells), Moscow: Nedra Publ., 1964, 154 p.

5. Joshi S.D., Augmentation of well productivity with slant and horizontal wells, SPE-15375-PA, 1988.

6. Renard G., Dupuy J.M., Formation damage effects on horizontalwell flow efficiency, SPE-19414-PA, 1991.

7. Nasybullin A.V., Lifant'ev A.V., Vasil'ev V.V., Astakhova A.N., Controlling over the model of liquid stable inflow towards a horizontal well and a crack of endless conductivity (In Russ.), Avtomatizatsiya, telemekhanizatsiya i svyaz' v neftyanoy promyshlennosti, 2014, no. 6, pp. 27–32.

8. Khasanov M.M., Mel'chaeva O.Yu., Roshchektaev A.P., Ushmaev O.S., Steady-state flow rate of horizontal wells in a line drive pattern (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2015, no. 1, pp. 48–51.

9. Galkin V.I., Ponomareva I.N., Chernykh I.A. et al., Methodology for estimating downhole pressure using multivariate model (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2019, no. 1, pp. 40–43.

10. Galkin V.I., Ponomareva I.N., Repina V.A., Study of oil recovery from reservoirs of different void types with use of multidimensional statistical analysis (In Russ.), Vestnik Permskogo natsional'nogo issledovatel'skogo politekhnicheskogo universiteta. Geologiya. Neftegazovoe i gornoe delo = Perm Journal of Petroleum and Mining Engineering, 2016, V. 15, no. 19, pp. 145–154, DOI: 10.15593/2224-9923/2016.19.5.

11. Galkin V.I., Ponomareva I.N., Koltyrin A.N., Development of probabilistic and statistical models for evaluation of the effectiveness of proppant hydraulic fracturing (on example of the Tl-Bb reservoir of the Batyrbayskoe field) (In Russ.), Vestnik Permskogo natsionalʹnogo issledovatelʹskogo politekhnicheskogo universiteta. Geologiya. Neftegazovoe i gornoe delo = Perm Journal of Petroleum and Mining Engineering, 2018, V. 17, no. 1, pp. 37–49, DOI: 10.15593/2224-9923/2018.1.4

12. Martyushev D.A., Ponomareva I.N., Researching features of development of fractured porous reservoirs reserves using well-test data (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2017, no. 10, pp. 102–104.

13. Ponomareva I.N., Martyushev D.A., Akhmetova M.I., Evaluation of the optimal duration of the hydrodynamic studies of low-productivity wells on the example of Ozernoye field (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2016, no. 1, pp. 60–63.

14. Ponomareva I.N., Martyushev D.A., Estimating reliability of reservoir properties determination on the basis of production analysis and pressure stabilization curves (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2019, no. 8, pp. 111–113.