Impact of sample geometry on the measurement of pressure-saturation curves: Experiments and simulations

• Published in: Water resources research 2015-11, Vol.51 (11), p.8900-8926
• Main Authors: Moura, M., Fiorentino, E.-A., Måløy, K. J., Schäfer, G., Toussaint, R.
• Format: Article
• Language: English
• Subjects: Aspect ratio; Boundaries; boundary effects; capillary flow; Capillary pressure; Computer simulation; Condensed Matter; Curves; Dimensions; Drainage measurement; Earth Sciences; flow in porous media; Fluid mechanics; Geophysics; Glycerol; Hydrology; Inlets (waterways); Mathematical models; Measurement; Mechanics; Multiphase flow; Percolation; Physics; Porous materials; Porous media; Pressure; Pressure measurement; pressure-saturation relationship; Saturation; Sciences of the Universe; Simulation; Soft Condensed Matter; Stress concentration; Water mixing; water retention curve
• ISSN: 0043-1397; 1944-7973; 1944-7973
• DOI: 10.1002/2015WR017196

In this paper, we study the influence of sample geometry on the measurement of pressure‐saturation relationships, by analyzing the drainage of a two‐phase flow from a quasi‐2‐D random porous medium. The medium is transparent, which allows for the direct visualization of the invasion pattern during flow, and is initially saturated with a viscous liquid (a dyed glycerol‐water mix). As the pressure in the liquid is gradually reduced, air penetrates from an open inlet, displacing the liquid which leaves the system from an outlet on the opposite side. Pressure measurements and images of the flow are recorded and the pressure‐saturation relationship is computed. We show that this relationship depends on the system size and aspect ratio. The effects of the system's boundaries on this relationship are measured experimentally and compared with simulations produced using an invasion percolation algorithm. The pressure build up at the beginning and end of the invasion process are particularly affected by the boundaries of the system whereas at the central part of the model (when the air front progresses far from these boundaries), the invasion happens at a statistically constant capillary pressure. These observations have led us to propose a much simplified pressure‐saturation relationship, valid for systems that are large enough such that the invasion is not influenced by boundary effects. The properties of this relationship depend on the capillary pressure thresholds distribution, sample dimensions, and average pore connectivity and its applications may be of particular interest for simulations of two‐phase flow in large porous media. Key Points: For large porous media, slow drainage happens at a constant capillary pressure Boundary effects can lead to changes in the invasion pattern and P‐S curves A simplified analytical expression for the P‐S curve is obtained