# SPE Journal Volume 16, Number 4, December 2011, pp. 795-811

SPE-132622-PA

### Modeling Gas-Phase Mass Transfer Between Fracture and Matrix in Naturally Fractured Reservoirs

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DOI  10.2118/132622-PA http://dx.doi.org/10.2118/132622-PA

### Citation

• Jamili, A., Willhite, G.P., and Green, D.W. 2011. Modeling Gas-Phase Mass Transfer Between Fracture and Matrix in Naturally Fractured Reservoirs. SPE J.  16 (4): 795-811. SPE-132622-PA. http://dx.doi.org/10.2118/132622-PA.

### Discipline Categories

• 6.4 Primary and Enhanced Recovery Processes
• 6.4.2 Gas-Injection Methods
• 6.4.7 Miscible Methods
• 6.3 Fluid Dynamics
• 6.3.1 Flow in Porous Media
• 6.3.2 Multi-phase Flow
• 6.2.1 Phase Behavior and PVT Measurements
• 6.2.2 Fluid Modeling, Equations of State

### Keywords

• Gas injection, Naturally fractured reservoir, Compositional simulation

### Summary

Gas injection in naturally fractured reservoirs maintains the reservoir pressure and increases oil recovery primarily by gravity drainage and to a lesser extent by mass transfer between the flowing gas in the fracture and the porous matrix. Although gravity drainage has been studied extensively, there has been limited research on mass-transfer mechanisms between the gas flowing in the fracture and fluids in the porous matrix.

This paper presents a mathematical model that describes the mass transfer between a gas flowing in a fracture and a matrix block. The model accounts for diffusion and convection mechanisms in both gas and liquid phases in the porous matrix. The injected gas diffuses into the porous matrix through gas and liquid phases, causing the vaporization of oil in the porous matrix, which is transported by convection and diffusion to the gas flowing in the fracture. Compositions of equilibrium phases are computed using the Peng-Robinson EOS.

The mathematical model was validated by comparing calculations to two sets of experimental data reported in the literature (Morel et. al. 1990; Le Romancer et. al. 1994), one involving nitrogen (N2) flow in the fracture and the second with carbon dioxide (CO2) flow. The matrix was a chalk. The resident fluid in the porous matrix was a mixture of methane and pentane. In the N2-diffusion experiment, liquid and vapor phases were initially present, while in the CO2 experiment, the matrix was saturated with liquid-hydrocarbon and water phases.

Calculated results were compared with the experimental data, including recovery of each component, saturation profiles, and pressure gradient between matrix and fracture. Agreement was generally good. The simulation revealed the presence of countercurrent flow inside the block. Diffusion was the main mass-transfer mechanism between matrix and fracture during N2 injection. In the CO2 experiment, diffusion and convection were both important.

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### History

• Original manuscript received: 8 April 2010
• Meeting paper published: 28 May 2010
• Revised manuscript received: 30 November 2010
• Manuscript approved: 1 December 2010
• Published online: 15 July 2011
• Version of record: 23 December 2011