# SPE Reservoir Evaluation & Engineering Volume 13, Number 3, June 2010, pp. 553-558

SPE-120104-PA

### Steady-State Productivity Equations for a Multiple-Wells System in Sector Fault Reservoirs

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DOI  10.2118/120104-PA http://dx.doi.org/10.2118/120104-PA

### Citation

• Lu, J., Ghedan, S., Zhu, T., Dinh, A., and Tiab, D. 2010. Steady-State Productivity Equations for a Multiple-Wells System in Sector Fault Reservoirs. SPE Res Eval & Eng  13 (3): 553-558. SPE-120104-PA. doi: 10.2118/120104-PA.

### Discipline Categories

• 5.1.4 Monitoring and Control

### Keywords

• Production and Operations, Steady-State, Productivity Equations, Multiple-Wells System, Sector Fault Reservoirs

### Summary

Currently in the oil industry, pseudosteady-state productivity equations for a multiple-wells system are used in all reservoir systems, regardless of the outer boundary conditions. However, if the reservoir is under edgewaterdrive, pseudosteady state is no longer applicable. When the producing time is sufficiently long, productivity equations based on the steady state are required.

This paper presents steady-state productivity equations for a multiple-wells system in homogeneous, anisotropic sector fault reservoirs. Taking fully penetrating vertical wells as uniform line sinks, and solving a square matrix of dimension n, where n is the number of wells, simple, reasonably accurate multiple-wells-system productivity equations are obtained. The proposed equations relate the production-rate vector to the pressure-drawdown vector and are applicable to a multiple-wells system, which is located arbitrarily in a sector fault reservoir. The analytical solutions are verified with reservoir numerical simulation in several examples. This paper also gives an equation for calculating skin factors of each well in steady state.

The analytical solutions perform well and match well with numerical solutions, and the benefit of the analytical model can be emphasized when the reservoir data deviate from their idealistic representation. It is concluded that the proposed equations provide a fast analytical tool to evaluate the performance of a multiple wells system in a sector fault reservoir.

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### History

• Original manuscript received: 24 November 2008
• Meeting paper published: 16 March 2008
• Revised manuscript received: 21 September 2009
• Manuscript approved: 3 December 2009
• Published online: 9 June 2010
• Version of record: 22 June 2010