During the field, development wells are regularly tested to measure production rate bottomhole pressure and water cut. Processing an array of these data measured over a sufficiently long period (of the order of a year) allows to get an estimate of the permeability distribution in the reservoir. This processing is based on singular decomposition of matrices, which another name is natural orthogonal functions. As the measurements have a local character the distribution of filtration properties will show good approximation with the reality when the well is located in a large, uniform area of the formation and values of the filtration properties will be rather average over the area, if in the area between wells there will be significant parts with strongly different filtration properties. The purpose of the work is to search the methods for assessing the distribution of the areas with the filtration heterogeneity zones with minimal interference with the reservoir. In the article it is shown that if after processing the production data of the wells an injection well in the vicinity of which it is necessary to explore the reservoir will be stimulated, and at the end of the excitation pulse to repeat data processing using natural orthogonal functions then it is possible to identify the potential areas with filtration heterogeneity. In addition, non-conductive faults in the vicinity of wells can be located. The duration of the exciting pulse is easy to evaluate, knowing the assessment of the permeability of the formation in the area of the well, obtained by processing a stationary case, and the size of the investigated area around the well. Using a model (simulated) example of a totally drilled field the possibility of determining filtration heterogeneity zones (bypassed zones) in the area between the working wells is shown. To obtain this the data from regular measurements of flow rate, bottomhole pressure are used, the flow rate of injection wells is varied and the method of natural orthogonal components using empirical data is applied. The simulated problem was considered, because in this case control is possible of the correctness of the solution of the problem and the validity of assumptions.

References

1. Bakhmutskiy M.L., Vol'pin S.G., Afanaskin I.V., Estimation of reservoir characteristics areal distribution by using bottom-hole pressure and flow-rate data in producing wells (In Russ), Neftepromyslovoe delo, 2018, no. 12, pp. 12–17.

2. Ashmyan K.D., Vol'pin S.G., Kovaleva O.V., Possible methods for estimating the composition, distribution and properties of residual oil during flooding (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2019, no. 8, pp. 114–117.

3. Basniev K.S., Kochina I.N., Maksimov V.M., Podzemnaya gidromekhanika (Underground fluid mechanics), Moscow: Nedra Publ., 1993, 416 p.

4. Golub G.H., van Loan C.F., Matrix computations, Johns Hopkins University Press; 1996, 784 p.

5. Ayvazyan S.A., Bukhshtaber V.M., Enyukov I.S. et al., Prikladnaya statistika. Klassifikatsiya i snizhenie razmernosti (Applied statistics. Classification and Dimension Reduction), Moscow: Finansy i statistika Publ., 1989, 607 p.

6. Meshcherskaya A.V., Rukhovets L.V., Yudin M.I. et al., Estestvennye sostavlyayushchie meteorologicheskikh poley (Natural components of meteorological fields), Leningrad: Gidrometeoizdat Publ., 1970, 199 p.

7. Forsythe G.E., Malcolm M.A., Moler C.B., Computer methods for mathematical computations, Prentice Hall, 1977, 270 p.

8. Kobayashi M., Dupret G., King O., Estimation of singular values of very large matrices using random sampling, Computers and Mathematics with Applications, 2001, V. 42, pp. 1331–1352.

9. Bakhmutskiy M.L., Nakhozhdenie singulyarnogo razlozheniya bol'shikh matrits (Finding a singular decomposition of large matrices), Proceedings of 41th international workshop session “Voprosy teorii i praktiki geologicheskoy interpretatsii gravitatsionnykh, magnitnykh i elektricheskikh poley” (Questions of the theory and practice of the geological interpretation of gravitational, magnetic and electric fields) named by D.G. Uspensky, 2014, pp. 36–37.

During the field, development wells are regularly tested to measure production rate bottomhole pressure and water cut. Processing an array of these data measured over a sufficiently long period (of the order of a year) allows to get an estimate of the permeability distribution in the reservoir. This processing is based on singular decomposition of matrices, which another name is natural orthogonal functions. As the measurements have a local character the distribution of filtration properties will show good approximation with the reality when the well is located in a large, uniform area of the formation and values of the filtration properties will be rather average over the area, if in the area between wells there will be significant parts with strongly different filtration properties. The purpose of the work is to search the methods for assessing the distribution of the areas with the filtration heterogeneity zones with minimal interference with the reservoir. In the article it is shown that if after processing the production data of the wells an injection well in the vicinity of which it is necessary to explore the reservoir will be stimulated, and at the end of the excitation pulse to repeat data processing using natural orthogonal functions then it is possible to identify the potential areas with filtration heterogeneity. In addition, non-conductive faults in the vicinity of wells can be located. The duration of the exciting pulse is easy to evaluate, knowing the assessment of the permeability of the formation in the area of the well, obtained by processing a stationary case, and the size of the investigated area around the well. Using a model (simulated) example of a totally drilled field the possibility of determining filtration heterogeneity zones (bypassed zones) in the area between the working wells is shown. To obtain this the data from regular measurements of flow rate, bottomhole pressure are used, the flow rate of injection wells is varied and the method of natural orthogonal components using empirical data is applied. The simulated problem was considered, because in this case control is possible of the correctness of the solution of the problem and the validity of assumptions.

References

1. Bakhmutskiy M.L., Vol'pin S.G., Afanaskin I.V., Estimation of reservoir characteristics areal distribution by using bottom-hole pressure and flow-rate data in producing wells (In Russ), Neftepromyslovoe delo, 2018, no. 12, pp. 12–17.

2. Ashmyan K.D., Vol'pin S.G., Kovaleva O.V., Possible methods for estimating the composition, distribution and properties of residual oil during flooding (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2019, no. 8, pp. 114–117.

3. Basniev K.S., Kochina I.N., Maksimov V.M., Podzemnaya gidromekhanika (Underground fluid mechanics), Moscow: Nedra Publ., 1993, 416 p.

4. Golub G.H., van Loan C.F., Matrix computations, Johns Hopkins University Press; 1996, 784 p.

5. Ayvazyan S.A., Bukhshtaber V.M., Enyukov I.S. et al., Prikladnaya statistika. Klassifikatsiya i snizhenie razmernosti (Applied statistics. Classification and Dimension Reduction), Moscow: Finansy i statistika Publ., 1989, 607 p.

6. Meshcherskaya A.V., Rukhovets L.V., Yudin M.I. et al., Estestvennye sostavlyayushchie meteorologicheskikh poley (Natural components of meteorological fields), Leningrad: Gidrometeoizdat Publ., 1970, 199 p.

7. Forsythe G.E., Malcolm M.A., Moler C.B., Computer methods for mathematical computations, Prentice Hall, 1977, 270 p.

8. Kobayashi M., Dupret G., King O., Estimation of singular values of very large matrices using random sampling, Computers and Mathematics with Applications, 2001, V. 42, pp. 1331–1352.

9. Bakhmutskiy M.L., Nakhozhdenie singulyarnogo razlozheniya bol'shikh matrits (Finding a singular decomposition of large matrices), Proceedings of 41th international workshop session “Voprosy teorii i praktiki geologicheskoy interpretatsii gravitatsionnykh, magnitnykh i elektricheskikh poley” (Questions of the theory and practice of the geological interpretation of gravitational, magnetic and electric fields) named by D.G. Uspensky, 2014, pp. 36–37.