Pressure Pulse in a Tight Rock Plug – Darcy’s Law with Klinkenberg Effect

2D_Plug_DL-oil-water_v5.2_Imbibition-Vertical_mesh
Figure 1. Mesh.

A tight sandstone core plug at zero water saturation is mounted in a pressure test cell. The sample chamber is filled with nitrogen gas. A known square pressure pulse is applied at the top of the core plug, and the pressure response is probed at its opposite end. The side surface of the core plug is wrapped in an impermeable sleeve.

The parameters for the considered sample correspond to core plug 4-51 as reported in SPE 89867: the diameter and length are 3.765 and 4.525 cm, respectively, the porosity is 11%, and the Klinkenberg-corrected permeability is taken to be K0 = 0.0632 mD. The gas slippage factor b is calculated using the correlation proposed by Jones and Owens (SPE-7551-PA): b = 0.86 K0-0.33 (with K0 in mD and b in atm), which corresponds to a value of 31.73 psi.

The system is at room temperature, and the applied pressure pulse has a mean value of 500 psi and an amplitude of 250 psi.
This two-dimensional model employs Cartesian coordinates.

Figure 2 shows the pressure transient response at the bottom of the sample chamber, for the applied pressure waveform at its top, for the cases without slippage correction (b = 0, green curve) and with the Klinkenberg correction (red curve).

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Figure 2. Pressure transient response with and without gas slippage correction.

The movie below shows the pressure distribution throughout the sample chamber, for the first 50 seconds of the experiment.

Movie. Pressure distribution throughout the sample chamber.
Movie. Pressure distribution throughout the sample chamber.

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