# SPE Journal Volume 17, Number 2, June 2012, pp. 631-652

SPE-128021-PA

### 2D Analytical Solution of Ideal Perforation Flow

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DOI  10.2118/128021-PA http://dx.doi.org/10.2118/128021-PA

### Citation

• Li, B., Sun, D., Gladkikh, M., and Wu, J. 2012. 2D Analytical Solution of Ideal Perforation Flow. SPE J.  17 (2): 631-652. SPE-128021-PA. http://dx.doi.org/10.2118/128021-PA.

### Discipline Categories

• 1.2 Drilling Design and Analysis
• 6.5 Reservoir Simulation
• 6.9 Unconventional Hydrocarbon Recovery
• 6.3 Fluid Dynamics
• 6.6 Reservoir Monitoring/Formation Evaluation

### Keywords

• ideal perforation flow, core flow efficiency, analytical solution

### Summary

Core-flow efficiency (CFE) is defined to quantitatively evaluate the flow performance of single-shot perforation. To calculate CFE, the flow rate of the ideal perforation flow in the core target is needed. The ideal flow rate is typically calculated with numerical simulators, but the computation may be time consuming and costly.

This paper presents the 2D analytical solution of the steady-state flow model (mass-conservation equation) for an ideal single-shot perforation in a cylindrical core sample. The separation-of-variable method is used to solve the partial-differential equation (PDE) of the flow model. Pressure and velocity distributions in (r, z) space are obtained, along with the flow-rate distribution along the perforation tunnel.

The accuracy and convergence of the analytical solution for ideal single-shot perforation flow are investigated and compared with those of the numerical solution of the commercial software ANSYS Fluent (ANSYS Fluent 12.0 User's Guide 2001). The analytical solution for the governing equation of ideal perforation flow is composed of an infinite number of Bessel functions. To compute CFE by making use of this analytical solution, the analytical solution is approximated with a limited number of Bessel functions. The approximated analytical solution is analyzed and compared with the numerical solutions from ANSYS Fluent.

Further, the axial-, radial-, and radial/axial-flow geometries of an ideal single-shot perforation are characterized with their approximated analytical solutions. Interactions between the boundary condition, perforation parameters, and core parameters are investigated for these flow geometries.

The analysis results show that: (1) The analytical solution has no grid effects, (2) the boundary condition of the perforated core is the dominant factor in the ideal flow rate of the perforated core, and (3) the penetration depth and anisotropic permeability are the significant factors in the flow performance of the perforated core.

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### History

• Original manuscript received: 17 February 2010
• Meeting paper published: 11 February 2010
• Revised manuscript received: 7 July 2011
• Manuscript approved: 22 July 2011
• Published online: 16 April 2012
• Version of record: 11 June 2012