An approach to solving the optimization problem for a multistage hydraulic fracturing (MHF) design is proposed. Free optimization parameters are set as follows: the length of the horizontal well, the number of fractures and the amount of proppant loaded in each fracture. Optimization targets are the maximum of the cumulative well production, the maximum of the net present value (NPV), and the minimum of fracturing costs. As an optimization algorithm, we use genetic algorithm NGSA-II, which requires calculating three related values at each iteration step: the fracture geometry, the post-fracture well production, and economy indicators. The approach proposed is illustrated by the case of the low-permeability oil reservoir under the following suggestions. It is assumed that the oil reservoir is rectangular, the horizontal well is positioned along the centerline of the reservoir, and hydraulic fractures are placed on equal distance perpendicular to the wellbore and symmetric about it. In addition, all fractures are identical to each other. The geometric characteristics of fractures (length and width) are determined by the amount of proppant injected and are calculated by empirical relationships. To obtain the value of post-fracture well production, approximate analytical formulas that take into account the final conductivity of fractures are applied. The main economic indicator that characterizes the economic profitability of the MHF is the NPV-based income. The case studies for different values of the average permeability of the reservoir are carried out. The numerical results show that the dependence of NPV on the well production is not always linear. The results show that after certain adjustment of the algorithm to parameters of the particular field, the model can be used as a tool for planning of the field development.

References

1. Economides M.J., Oligney R.E., Valko P.P., Unified fracture design: Bridging the gap between theory and practice, Texas: Orsa Press Alvin, 2002, 262 p.

2. Marongiu-Porcu M., Economides M.J., Holditch S.A., Economic and physical optimization of hydraulic fracturing, J. Nat. Gas. Sci. Eng., 2013, V. 14, pp. 91–107.

3. Rahman M.M., Rahman M.K., Rahman S.S., An integrated model for multiobjective design optimization of hydraulic fracturing, J. Petrol. Sci. Eng., 2001, V. 31, pp. 41–62.

4. Rahman M.M., Rahman M.K., Rahman S.S., Multicriteria hydraulic fracturing optimization for reservoir stimulation, Pet. Sci. Technol., 2003, V. 21, pp. 1721–1758.

5. Deb K., Agrawal S., Pratap A. et al., A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans. Evol. Comp., 2002, V. 6, pp. 182–197.

6. Shel E. et al., Retrospective analysis of hydrofracturing with the dimensionless parameters: Comparing design and transient tests (In Russ.), SPE 191707-18RPTC-MS, 2018, https://doi.org/10.2118/191707-18RPTC-MS.

7. Shel E.V., Paderin G.V., Kabanova P.K., Testing methodology for the hydrofracturing simulator (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2018, no. 12, pp. 42–45.

8. Elkin S.V., Aleroev A.A., Veremko N.A. et.al., Flowrate calculation model for fractured horizontal well depending on frac stages number (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2016, no. 1, pp. 64–67.

9. Elkin S.V., Aleroev A.A., Veremko N.A. et.al., Accounting for dimensionless conductivity in express calculation of flow-rate in a well after multi-stage hydraulic fracturing (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2016, no. 12, pp. 110–113.

An approach to solving the optimization problem for a multistage hydraulic fracturing (MHF) design is proposed. Free optimization parameters are set as follows: the length of the horizontal well, the number of fractures and the amount of proppant loaded in each fracture. Optimization targets are the maximum of the cumulative well production, the maximum of the net present value (NPV), and the minimum of fracturing costs. As an optimization algorithm, we use genetic algorithm NGSA-II, which requires calculating three related values at each iteration step: the fracture geometry, the post-fracture well production, and economy indicators. The approach proposed is illustrated by the case of the low-permeability oil reservoir under the following suggestions. It is assumed that the oil reservoir is rectangular, the horizontal well is positioned along the centerline of the reservoir, and hydraulic fractures are placed on equal distance perpendicular to the wellbore and symmetric about it. In addition, all fractures are identical to each other. The geometric characteristics of fractures (length and width) are determined by the amount of proppant injected and are calculated by empirical relationships. To obtain the value of post-fracture well production, approximate analytical formulas that take into account the final conductivity of fractures are applied. The main economic indicator that characterizes the economic profitability of the MHF is the NPV-based income. The case studies for different values of the average permeability of the reservoir are carried out. The numerical results show that the dependence of NPV on the well production is not always linear. The results show that after certain adjustment of the algorithm to parameters of the particular field, the model can be used as a tool for planning of the field development.

References

1. Economides M.J., Oligney R.E., Valko P.P., Unified fracture design: Bridging the gap between theory and practice, Texas: Orsa Press Alvin, 2002, 262 p.

2. Marongiu-Porcu M., Economides M.J., Holditch S.A., Economic and physical optimization of hydraulic fracturing, J. Nat. Gas. Sci. Eng., 2013, V. 14, pp. 91–107.

3. Rahman M.M., Rahman M.K., Rahman S.S., An integrated model for multiobjective design optimization of hydraulic fracturing, J. Petrol. Sci. Eng., 2001, V. 31, pp. 41–62.

4. Rahman M.M., Rahman M.K., Rahman S.S., Multicriteria hydraulic fracturing optimization for reservoir stimulation, Pet. Sci. Technol., 2003, V. 21, pp. 1721–1758.

5. Deb K., Agrawal S., Pratap A. et al., A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans. Evol. Comp., 2002, V. 6, pp. 182–197.

6. Shel E. et al., Retrospective analysis of hydrofracturing with the dimensionless parameters: Comparing design and transient tests (In Russ.), SPE 191707-18RPTC-MS, 2018, https://doi.org/10.2118/191707-18RPTC-MS.

7. Shel E.V., Paderin G.V., Kabanova P.K., Testing methodology for the hydrofracturing simulator (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2018, no. 12, pp. 42–45.

8. Elkin S.V., Aleroev A.A., Veremko N.A. et.al., Flowrate calculation model for fractured horizontal well depending on frac stages number (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2016, no. 1, pp. 64–67.

9. Elkin S.V., Aleroev A.A., Veremko N.A. et.al., Accounting for dimensionless conductivity in express calculation of flow-rate in a well after multi-stage hydraulic fracturing (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2016, no. 12, pp. 110–113.