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Flow measurement in porous media is a challenging subject, especially when it comes to performing a three-dimensional (3D) velocimetry at the micro scale. Volumetric flow measurement techniques such as defocusing and tomographic imaging generally involve rigorous procedures, complex experimental setups, and multi-part data processing procedures. However, detailed knowledge of the flow pattern at the pore and subpore scales is important in interpreting the phenomena that occur inside the porous media and understanding the macro-scale behaviors. In this work, the flow of an oil inside a porous medium is measured at the pore and subpore scales using refractive index matching (RIM) and shadowgraph imaging techniques. At the macro scale, flow is measured using the particle image velocimetry (PIV) method in two dimensions (2D) to confirm the volumetric nature of the flow and obtain the overall flow pattern in the vicinity of the flow entrance and at the far field. At the micro scale, the three-dimensional (3D) flow within an arbitrary volume of the porous medium was quantified using 2D particle-tracking velocimetry (PTV) utilizing the law of conservation of mass. Using the shadowgraphy method and a single camera makes the flow measurement much less complex than the approaches using laser light sheets or multiple cameras with multiple viewing angles.

Micro- and Macro-Scale Measurement of Flow Velocity in Porous Media: A Shadow Imaging Approach for 2D and 3D