1. Relating Capillary Pressure to Interfacial Curvature Using a Two-dimensional Micromodel
Kendra I. Brown, Dorthe Wildenschild, and Mark L. Porter
H41F-0935
Department of Chemical, Biological and Environmental Engineering, Oregon State University, Corvallis, Oregon
Experimental Setup
Relaxing Interfaces
Introduction
Capillary pressure plays a critical role in multiphase flow and transport in porous media. Because it is defined as the difference in wetting and non-wetting fluid pressures, it is also a function of both saturation and the interfacial area between the wetting and non-wetting phases. Experiments were performed in a two-dimensional micro-scale porous medium to gain insight into the relationship between externally measured capillary pressure and internally measured interfacial curvature.
High-resolution images of phase distributions and associated interfaces within the pores are collected during drainage and imbibition experiments. Images with approximately 1 μm-resolution are acquired at regular intervals during the relaxation process. Concurrently, pressure in each phase is measured with a transducer outside the porous medium, and Laplace’s Law is used to calculate the average pressure inside the porous medium based on measured curvatures, such that the two pressure values can be compared. The relaxation of capillary pressure can then be correlated to the relaxation of interface menisci for varying degrees of system saturation, and for varying flow rates.
The images and capillary pressure measurements will allow for investigation of pore scale properties during dynamic flow conditions, as well as static conditions, and importantly, allow for comparison among the two situations.
Etched lithography micro-model (penny shown for scale). The vertical spacing is 50 micron.
Microscope and Camera
UV Light
Pressure Transducer
Image Processing and Curvature Calculation
Micromodel
Pump
Dry image processing
Light Source
The micromodel was compressed between two plates to seal the inlet and outlet ports. Soltrol 220, an LNAPL, was pumped into the flow cell at rates ranging from 0.1 to 10 μL/min. The soltrol was mixed with an oil-soluble fluorescent dye (“Carquest UV Detector Dye”) to contrast the oil and air phases under UV light.
Raw image
Segmented
Dilated
Inverted
Capillary Pressure and Interfacial Curvature
Labelled
Segmented + labelled
Solids only
Registered to wet image
Example Images r
Pliquid
Pgas
Wet image processing
Images of the oil-water interfaces were taken during flow and equilibration. Pressure was simultaneously measured with a transducer outside of the system. Example images are shown below and in the accompanying video clip.
Raw image
Segmented
w. solids overlay
Data for curvature algorithm
Two-dimensional Micromodel
Wetting phase
Nonwetting phase
Solid phase
Future Work
Calibration and verification of curvature algorithm on both high and low resolution
images
Improved flow control
Evaluate capillary pressure based on curvature against capillary pressure measured
outside the model with a transducer
Run experiments for static and dynamic flow conditions, and at different flow rates
Measure interface relaxation for different flow rates
Compare experimental flow behavior with Lattice-Boltzmann simulations
Preliminary Measurements A B
Pressures are measured with a transducer outside of the system as the interface progresses from image A to B, which is shown in the accompanying video clip.
Six porous media patterns were photo-etched into a silicon wafer to a depth of 50 microns. A layer of silicon dioxide was grown on the surface, and a glass plate anodically bonded to the wafer to create hydrophilic flow channels. The micromodels were produced by Washington Technology Center.
By measuring the interface curvatures in the images, the expected capillary pressures were calculated via the Laplace Equation.
Acknowledgments
Thanks to Dr. Laura Pyrak-Nolte for providing the curvature code, financial support from NSF EAR , including REU Supplement, OSU URISC support.