Abstract
The pore and pore-throat sizes of shale and tight rock formations are on the order of tens of nanometers. The fluid flow in such small pores is significantly affected by walls of pores and pore-throats. This boundary layer effect on fluid flow in tight rocks has been investigated through laboratory work on capillary tubes. It is observed that low permeability is associated with large boundary layer effect on fluid flow. The experimental results from a single capillary tube are extended to a bundle of tubes and finally to porous media of tight formations. A physics-based, non-Darcy low-velocity flow equation is derived to account for the boundary layer effect of tight reservoirs by adding a non-Darcy coefficient term. This non-Darcy equation describes the fluid flow more accurately for tight oil reservoir with low production rate and low pressure gradient. Both analytical and numerical solutions are obtained for the new non-Darcy flow model. First, a Buckley–Leverett-type analytical solution is derived with this non-Darcy flow equation. Then, a numerical model has been developed for implementing this non-Darcy flow model for accurate simulation of multidimensional porous and fractured tight oil reservoirs. Finally, the numerical studies on an actual field example in China demonstrate the non-negligible effect of boundary layer on fluid flow in tight formations.
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Appendix: Experimental Setup and Procedure
Appendix: Experimental Setup and Procedure
The experimental method and setup is the same as the work of Xu and Yue (2007), and the experimental apparatus is shown in Fig. 13.
Experimental setup. Modified according to Xu and Yue (2007)
It consists of three parts, driving force system, filtering system and measurement system. They are separated by the dash lines in the sketch of experimental setup as shown in Fig. 13. Pressurized nitrogen gas is used as the driving force. It is filtered in the gas filtering system and reaches to liquid tank to drive the deionized water in the tank. The moving deionized water is also filtered and reaches to the small capillary tube. The flow rate of capillary tube is measured by observing the change of liquid level in liquid measurement tube and recording the corresponding time. The liquid level is magnified with microscope and transferred to the graphic display in the computer. With the measured flow rate and pressure gradient along the tube, the thickness of boundary flow can be calculated.
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Xiong, Y., Yu, J., Sun, H. et al. A New Non-Darcy Flow Model for Low-Velocity Multiphase Flow in Tight Reservoirs. Transp Porous Med 117, 367–383 (2017). https://doi.org/10.1007/s11242-017-0838-8
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DOI: https://doi.org/10.1007/s11242-017-0838-8