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The forecast of the flow rate of horizontal wells under nonlinear filtering conditions

UDK: 622.276.3
DOI: 10.24887/0028-2448-2020-6-72-75
Key words: horizontal well, nonlinear filtering, oil production rate, forecast of oil production
Authors: O.N. Shevchenko (VolgogradNIPImorneft Branch of LUKOIL-Engineering LLC)

Recently, it is necessary to note the presence of negative dynamics in the deterioration of the structure of reserves of newly discovered fields, and most of the latter are already classified as hard-to-recover, confined to develop with a complex geological structure, low permeability, and high oil viscosity, complicated by the presence of faults, active plantar waters and gas caps. Drilling of hard-to-recover reserves takes place with horizontal wells. It is quite difficult to reliably predict the parameters of the operation of deposits, the performance of horizontal wells obtained with the help of modern hydrodynamic stimulators is unreliable, which ultimately leads to the formation of an insufficiently rational development system, and the resulting complications during operation in field conditions have to be solved at the expense of significant amounts of material and labor resources. One of the main parameters when making a technical and economic assessment of a reservoir is the flow rate of each horizontal well taken separately. Analytical methods for calculating the horizontal well flow rate show a high error due to the use of the classical linear filtration law, whereas under these conditions, fluid filtration cannot be described by the linear Darcy law. In conditions of high-viscosity oils and a low-permeable reservoir, there is an initial pressure gradient due to the rheological properties of the filtered liquid and high values of the surface friction coefficient. In the conditions of a thin oil fringe and an increased gas factor, the limiting filtration rates are observed due to the mode of dissolved gas, and the flow of fluid is described by a nonlinear law. It is proposed to take a new look at the problem of determining the forecast flow rate of a horizontal well, using known approaches to solving this issue.

References

1. Basniev K.S., Kochina I.N., Maksimov V.M., Podzemnaya gidromekhanika

(Underground fluid mechanics), Moscow: Nedra Publ., 1993, 416 p.

2. Barenblatt G.I., Entov V.M., Ryzhik V.M., Dvizhenie zhidkostey i gazov v prirodnykh plastakh (Movement of liquids and gases in natural reservoirs), Moscow: Nedra Publ., 1982, 211 p.

3. Khristianovich S.A., Groundwater movement not following Darcy's law

(In Russ.), Prikladnaya matematika i mekhanika, 1940, V. 4, no. 1, pp. 33–52.

4. Basniev S.K., Dmitriev N.M., Rozenberg G.D., Neftegazovaya gidromekhanika (Oil and gas hydromechanics), Moscow-Izhevsk: Publ. of Institute of Computer Science, 2005, 544 p.

5. Butler R.M., Horizontal wells for the recovery of oil, gas and bitumen, Petroleum Society of CIM, Monograph no. 2, 1994.

6. Voronich I.V., Gaydukov L.A., Mikhaylov N.N., Fluid filtration to a horizontal well with variation in the parameters of the damage zone (In Russ), Prikladnaya mekhanika i tekhnicheskaya fizika = Journal of Applied Mechanics and Technical Physics, 2011, V. 52, no. 4, pp. 127–135.

7.В  Chernykh V.A., Chernykh V.V., Matematicheskie modeli gorizontal'nykh i naklonnykh gazovykh skvazhin (Mathematical models of horizontal and inclined gas wells), Moscow: Neft' i gaz Publ., 2008, 460 p.

8. Khristianovich S.A., Gal'perin V.G., Millionshchikov M.D. et al., Prikladnaya gazovaya dinamika (Applied gas dynamics), Moscow: Publ. of TsAGI, 1948, 148 p.

9. Bernadiner M.G., Entov V.M., Gidrodinamicheskaya teoriya fil'tratsii anomal'nykh zhidkostey (Hydrodynamic theory of the filtration of anomalous liquids), Moscow: Nauka Publ., 1975, 197 p.

10. Koroteev M.V., Matematicheskoe modelirovanie gidrodinamicheskikh fil'tratsionnykh techeniy k gorizontal'nym skvazhinam pri nelineynykh zakonakh soprotivleniya sredy (Mathematical modeling of hydrodynamic filtration flows to horizontal wells with nonlinear laws of medium resistance): thesis of candidate of physical and mathematical science,В  Moscow, 2004.

11. Markitantova N.A., Chernyaev A.P., Nonlinear filtration to a horizontal well in the case of special nonlinearity (In Russ.), Trudy Moskovskogo fiziko-tekhnicheskogo instituta = Proceedings of MIPT, 2011, V. 3, no. 1, pp. 88–92.

12. Markitantova N.A., Chernyaev A.P., Filtration with a power law in the case of asymmetrical wellsite (In Russ.), Trudy Moskovskogo fiziko-tekhnicheskogo instituta = Proceedings of MIPT, 2013, V. 5, no. 4, pp. 151–160.


Recently, it is necessary to note the presence of negative dynamics in the deterioration of the structure of reserves of newly discovered fields, and most of the latter are already classified as hard-to-recover, confined to develop with a complex geological structure, low permeability, and high oil viscosity, complicated by the presence of faults, active plantar waters and gas caps. Drilling of hard-to-recover reserves takes place with horizontal wells. It is quite difficult to reliably predict the parameters of the operation of deposits, the performance of horizontal wells obtained with the help of modern hydrodynamic stimulators is unreliable, which ultimately leads to the formation of an insufficiently rational development system, and the resulting complications during operation in field conditions have to be solved at the expense of significant amounts of material and labor resources. One of the main parameters when making a technical and economic assessment of a reservoir is the flow rate of each horizontal well taken separately. Analytical methods for calculating the horizontal well flow rate show a high error due to the use of the classical linear filtration law, whereas under these conditions, fluid filtration cannot be described by the linear Darcy law. In conditions of high-viscosity oils and a low-permeable reservoir, there is an initial pressure gradient due to the rheological properties of the filtered liquid and high values of the surface friction coefficient. In the conditions of a thin oil fringe and an increased gas factor, the limiting filtration rates are observed due to the mode of dissolved gas, and the flow of fluid is described by a nonlinear law. It is proposed to take a new look at the problem of determining the forecast flow rate of a horizontal well, using known approaches to solving this issue.

References

1. Basniev K.S., Kochina I.N., Maksimov V.M., Podzemnaya gidromekhanika

(Underground fluid mechanics), Moscow: Nedra Publ., 1993, 416 p.

2. Barenblatt G.I., Entov V.M., Ryzhik V.M., Dvizhenie zhidkostey i gazov v prirodnykh plastakh (Movement of liquids and gases in natural reservoirs), Moscow: Nedra Publ., 1982, 211 p.

3. Khristianovich S.A., Groundwater movement not following Darcy's law

(In Russ.), Prikladnaya matematika i mekhanika, 1940, V. 4, no. 1, pp. 33–52.

4. Basniev S.K., Dmitriev N.M., Rozenberg G.D., Neftegazovaya gidromekhanika (Oil and gas hydromechanics), Moscow-Izhevsk: Publ. of Institute of Computer Science, 2005, 544 p.

5. Butler R.M., Horizontal wells for the recovery of oil, gas and bitumen, Petroleum Society of CIM, Monograph no. 2, 1994.

6. Voronich I.V., Gaydukov L.A., Mikhaylov N.N., Fluid filtration to a horizontal well with variation in the parameters of the damage zone (In Russ), Prikladnaya mekhanika i tekhnicheskaya fizika = Journal of Applied Mechanics and Technical Physics, 2011, V. 52, no. 4, pp. 127–135.

7.В  Chernykh V.A., Chernykh V.V., Matematicheskie modeli gorizontal'nykh i naklonnykh gazovykh skvazhin (Mathematical models of horizontal and inclined gas wells), Moscow: Neft' i gaz Publ., 2008, 460 p.

8. Khristianovich S.A., Gal'perin V.G., Millionshchikov M.D. et al., Prikladnaya gazovaya dinamika (Applied gas dynamics), Moscow: Publ. of TsAGI, 1948, 148 p.

9. Bernadiner M.G., Entov V.M., Gidrodinamicheskaya teoriya fil'tratsii anomal'nykh zhidkostey (Hydrodynamic theory of the filtration of anomalous liquids), Moscow: Nauka Publ., 1975, 197 p.

10. Koroteev M.V., Matematicheskoe modelirovanie gidrodinamicheskikh fil'tratsionnykh techeniy k gorizontal'nym skvazhinam pri nelineynykh zakonakh soprotivleniya sredy (Mathematical modeling of hydrodynamic filtration flows to horizontal wells with nonlinear laws of medium resistance): thesis of candidate of physical and mathematical science,В  Moscow, 2004.

11. Markitantova N.A., Chernyaev A.P., Nonlinear filtration to a horizontal well in the case of special nonlinearity (In Russ.), Trudy Moskovskogo fiziko-tekhnicheskogo instituta = Proceedings of MIPT, 2011, V. 3, no. 1, pp. 88–92.

12. Markitantova N.A., Chernyaev A.P., Filtration with a power law in the case of asymmetrical wellsite (In Russ.), Trudy Moskovskogo fiziko-tekhnicheskogo instituta = Proceedings of MIPT, 2013, V. 5, no. 4, pp. 151–160.




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